References - Lehrstuhl Numerische Mathematik - TUM

References
Abraham, R., J. E. Marsden, and T. Ratiu (1988). Manifolds, Tensor Analysis, and Applications
(2nd ed.). New York, NY: Springer–Verlag.
Alexander, R. (1977). Diagonally implicit Runge–Kutta methods for stiff ODEs. SIAM J. Nu-
mer. Anal. 14, 1006–1021.
Alishenas, T. and O. Olafson (1994). Modelling and velocity stabilization of constrained me-
chanical systems. BIT 34, 455–483.
Alligood, K. T. and J. A. Yorke (1986). Hopf bifurcation: The appearance of virtual periods in
cases of resonance. J. Diff. Equations 64, 375–394.
Arevalo, C. (1993). Matching the structure of DAEs and Multistep methods. Ph. D. thesis, Lund
Univ., Lund, Sweden.
Arnold, V. I. (1983). Geometrical Methods in the Theory of Ordinary Differential Equations,
Volume 250 of Grundlehren Mathem. Wiss. New York, NY: Springer–Verlag.
Arnold, V. I., S. M. Gusein-Zade, and A. N. Varchenko (1985). Singularities of Differentiable
Maps, Vol. I. Boston, MA: Birkhäuser Verlag. Translation from the Russian.
Ascher, U. M., H. Chin, L. R. Petzold, and S. Reich (1995). Stabilization of constrained mechan-
ical systems with DAEs and invariant manifolds. J. Mech. Struct. Machines 23, 135–158.
Ascher, U. M., H. Chin, and S. Reich (1994). Stabilization of DAEs and invariant manifolds.
Numer. Math. 67, 131–149.
Ascher, U. M., J. Christiansen, and R. D. Russell (1979). A collocation solver for a mixed order
boundary value ODE solver. Math. of Comp. 33, 659–679.
Ascher, U. M., R. M. M. Mattheij, and R. D. Russell (1995). Numerical Solution of Boundary
Value Problems for Ordinary Differential Equations, Volume 13 of Classics in Appl. Mathem.
Philadelphia, PA: SIAM Publications.
Ascher, U. M. and L. R. Petzold (1991). Projected implicit Runge–Kutta methods for
differential–algebraic equations. SIAM J. Numer. Anal. 28, 1097–1120.
Ascher, U. M. and L. R. Petzold (1998). Computer Methods for Ordinary Differential Equations
and Differential–Algebraic Equations. Philadelphia, PA: SIAM Publications.
Ascher, U. M. and S. Reich (1998). On some difficulties in integrating highly oscillatory Hamil-
tonian systems. In Lect. Notes in Comp. Sci. and Eng., Volume 4, pp. 281–296. New York,
NY: Springer–Verlag.
Ascher, U. M. and R. Spiteri (1994). Collocation software for boundary value differential–
algebraic equations. SIAM J. Sci. Stat. Comp. 15, 938–952.
339

REFERENCES 340
Bader, G. and U. Ascher (1987). A new basis implementation for a mixed order boundary value
ODE solver. SIAM J. Sci. Stat. Comp. 8, 483–500.
Bauer, I., H. G. Bock, S. Körkel, and J. P. Schlöder (1999). Numerical methods for initial
value problems and derivative generation for DAE models with application to optimum
experimental design of chemical processes. In Proc. Int. Workshop on Scient. Comput. in
Chem. Engin., Volume II. TU Hamburg Harburg, Germany.
Bauer, I., H. G. Bock, D. B. Leineweber, and J. P. Schlöder (1999). Direct multiple shooting
methods for control and optimization of DAEs in chemical engineering. In Proc. Int. Work-
shop on Scient. Comput. in Chem. Engin., Volume II. TU Hamburg Harburg, Germany.
Baumgarte, J. (1972). Stabilization of constraints and integrals of motion in dynamical systems.
Comp. Meth. Appl. Mech. Eng. 1, 11–16.
Beardmore, R. E. (1998). Stability and bifurcation properties of index–1 DAEs. Numer. Algo-
rithms 19, 43–53.
Becker, T. and V. Weispfenning (1993). Gröbner Bases, a Computational Approach to Commu-
tative Algebra, Volume 141 of Grad. Texts in Mathem. New York, NY: Springer–Verlag.
Berzins, M. and R. M. Furzeland (1985). A user’s manual for SPRINT – a versatile software
package for solving systems of algebraic, ordinary, and partial differential equations. Tech-
nical Report TNER.85.058, Thornton Res. Centre, Shell Research Ltd.
Biegler, L. T. and J. J. Damiano (1986). Nonlinear parameter estimation: A case study. AIChE
Journal 32, 29–45.
Bishop, R. L. and R. J. Crittenden (1964). Geometry of Manifolds. New York, NY: Academic
Press.
Blajer, W. (1997). A geometric unification of constrained system dynamics. Multibody Syst.
Dynam. 1, 3–21.
Blajer, W. and A. Markiewicz (1995). The effect of friction on multibody dynamics. European
J. Mech. Solids 14, 807–825.
Bock, H. G., E. Eich, and J. P. Schlöder (1988). Numerical solution of constrained least squares
boundary value problems in differential–algebraic equations. In K. Strehmel (Ed.), Numer-
ical Treatment of Differential Equations. Leipzig, Germany: Teubner Verlag.
Bock, H. G. and K. J. Plitt (1984). A multiple shooting algorithm for direct solution of con-
strained optimal control problems. In Proc. 9th IFAC World Congress, Budapest, Hungary,
pp. 242–247. Pergamon Press.
Bock, H. G., J. P. Schlöder, M. C. Steinbach, and H. Wörn (1997). Schnelle Roboter am
Fliessband: Mathematische Bahnoptimierung in Praxis. In K. H. Hoffmann, W. Jäger,
T. Lohmann, and H. Schunck (Eds.), Mathematik Schlüsseltechnologie für die Zukunft, pp.
539–550. Berlin, Germany: Springer–Verlag.
Bornemann, F. A. (1998). Homogenization in Time of Singularly Perturbed Conservative Me-
chanical Systems, Volume 1687 of Lect. Notes in Math. New York, NY: Springer–Verlag.
Bremer, H. and P. Pfeiffer (1992). Elastische Mehrkörpersysteme. Stuttgart, Germany: Teubner
Verlag.
Brenan, K. E. (1983). Stability and convergence of difference approximations for higher index
differential algebraic systems with applications in trajectory control. Ph. D. thesis, Univ. of
Calif. at Los Angeles, Los Angeles, CA.

REFERENCES 341
Brenan, K. E., S. L. Campbell, and L. R. Petzold (1989). Numerical Solution of Initial–Value
Problems in Differential–Algebraic Equations. New York, NY: Elsevier Science Publ.
Brenan, K. E., S. L. Campbell, and L. R. Petzold (1996). Numerical Solution of Initial–Value
Problems in Differential–Algebraic Equations, Volume 14 of Classics in Appl. Math. Philadel-
phia, PA: SIAM Publications.
Brenan, K. E. and B. E. Enquist (1988). Backward differentiation approximations of nonlinear
differential/algebraic equations. Math. of Comp. 51, 659–676.
Brenan, K. E. and L. R. Petzold (1989). The numerical solution of higher index differen-
tial/algebraic equations by implicit Runge–Kutta methods. SIAM J. Numer. Anal. 26,
976–996.
Brown, P. N., A. C. Hindmarsh, and L. R. Petzold (1994). Using Krylov methods in the solution
of large–scale differential algebraic systems. SIAM J. Sci. Stat. Comp. 15, 1467–1488.
Burkardt, J. and W. C. Rheinboldt (1983). A locally parametrized continuation process. ACM
Trans. Math. Softw. 9, 215–235.
Burrage, K. and L. R. Petzold (1990). On order reduction for Runge–Kutta methods applied
to differential/algebraic systems and to stiff systems of ODEs. SIAM J. Numer. Anal. 27,
447–456.
Butcher, J. C. (1964). Implicit Runge–Kutta processes. Math. of Comp. 18, 50–64.
Byrne, G. D. and A. C. Hindmarsh (1987). Stiff ODE solvers: A review of current and coming
attractions. J. Comput. Phys. 70, 1–62.
Cameron, I. T. (1983). Solution of differential–algebraic systems using diagonally–implicit
Runge–Kutta methods. IMA J. Numer. Anal. 3, 273–289.
Campbell, S. L. (1980). Singular Systems of Differential Equations, I. London, UK: Pitman
Publ. Ltd.
Campbell, S. L. (1982). Singular Systems of Differential Equations, II. London, UK: Pitman
Publ. Ltd.
Campbell, S. L. (1985). The numerical solution of higher index linear time varying singular
systems of differential equations. SIAM J. Sci. Stat. Comp. 6, 334–348.
Campbell, S. L. (1987). A general form for solvable linear time varying singular systems of
differential equations. SIAM J. Math. Anal. 18, 1101–1115.
Campbell, S. L. and C. W. Gear (1995). The index of general nonlinear DAEs. Numer. Math. 72,
173–196.
Campbell, S. L. and E. Griepentrog (1995). Solvability of general differential algebraic equations.
SIAM J. Sci. Stat. Comp. 16, 257–270.
Campbell, S. L. and L. Petzold (1983). Canonical forms and solvable singular systems of diff-
erential equations. SIAM J. Alg. Disc. Meth. 4, 517–521.
Caracotsios, M. and W. E. Stewart (1985). Sensitivity analysis of initial value problems with
mixed ODEs and algebraic equations. Comp. and Chem. Eng. 9, 359–365.
Cartan, E. (1945). Les Systèmes Différentiels Extérieurs et Leurs Applications Géométriques.
Paris, France: Hermann.
Cash, J. R. (1980). On the integration of stiff systems of ODEs using extended backward
differentiation formulas. Numer. Math. 34, 235–246.

REFERENCES 342
Cavendish, J., C. A. Hall, W. C. Rheinboldt, and M. L. Wenner (1986). DEM: A new compu-
tational approach to sheet metal forming problems. Int. J. Num. Meth. Eng. 23, 847–862.
Chaperon, M. (1986). Géometrie Différentielle et Singularités de Systèmes Dynamiques, Volume
138–139 of Astérisque. Paris, France: Soc. Math. France.
Choquet-Bruhat, Y., C. De Witt-Morette, and M. Dillard-Bleick (1982). Analysis, Manifolds
and Physics, Part I. Amsterdam, The Netherlands: North–Holland.
Chua, L. O. and A.-C. Deng (1989a). Impasse points. Part I: Numerical aspects. Int. J. Circ.
Theor. and Appl. 17, 213–235.
Chua, L. O. and A.-C. Deng (1989b). Impasse points. Part II: Analytical aspects. Int. J. Circ.
Th. and Appl. 17, 271–282.
Chua, L. O. and H. Oka (1988). Normal forms for constrained nonlinear differential equations,
Part I: Theory. IEEE Trans. Circ. and Syst. 35, 881–901.
Chua, L. O. and H. Oka (1989). Normal forms for constrained nonlinear differential equations,
Part II: Bifurcation. IEEE Trans. Circ. and Syst. 36, 71–88.
Chua, L. O. and Y. Yu (1983). Negative resistance devices. Int. J. Circ. Theor. and Appl. 11,
162–186.
Clark, K. D. and L. R. Petzold (1989). Numerical solution of boundary value problems for
differential–algebraic systems. SIAM J. Sci. Stat. Comp. 10, 915–936.
Cobb, D. (1982). On the solutions of linear differential equations with singular coefficients. J.
Diff. Equations 42, 311–323.
Corduneanu, C. (1977). Principles of Differential and Integral Equations. New York, NY:
Chelsea Publ. Co.
Crandall, M. G. and P. H. Rabinowitz (1977). The Hopf bifurcation theorem in infinite dimen-
sions. Arch. Rat. Mech. Anal. 67, 53–72.
Crouch, P. E. and R. Grossman (1993). Numerical integration of ordinary differential equations
on manifolds. J. Nonlin. Sci. 3, 1–33.
Curtis, A. R. (1980). The FACSIMILE numerical integrator for stiff initial value problems. In
I. Gladwell and D. K. Sayers (Eds.), Computational Techniques for Ordinary Differential
Equations, pp. 47–82. London, UK: Academic Press.
Curtis, C. F. and J. O. Hirschfelder (1952). Integration of stiff equations. Proc. Nat. Acad.
Sci. 38, 235–243.
Dahlquist, G. (1956). Convergence and stability in the numerical integration of ordinary diff-
erential equations. Math. Scand. 4, 33–53.
Dahlquist, G. (1983). On one–leg multistep methods. SIAM J. Numer. Anal. 20, 1130–1138.
Darboux, G. (1873). Sur les solutions singulières des équations aux dérivées ordinaires du pre-
mier ordre. Bull. Sc. Math. Astron. 4, 158–176.
De Hoog, F. R. and R. M. M. Mattheij (1987). On dichotomy and well conditioning in BVP.
SIAM J. Numer. Anal. 24, 89–105.
Desoer, C. A. and F. F. Wu (1974). Nonlinear networks. SIAM J. Appl. Math. 26, 315–333.
Deuflhard, P. (1983). Order and stepsize control in extrapolation methods. Numer. Math. 41,
399–422.

REFERENCES 343
Deuflhard, P. (1985). Recent progress in extrapolation methods for ordinary differential equa-
tions. SIAM Rev. 27, 505–535.
Deuflhard, P., E. Hairer, and J. Zugck (1987). One–step and extrapolation methods for
differential–algebraic equations. Numer. Math. 51, 501–516.
Deuflhard, P. and U. Nowak (1987). Extrapolation integrators for quasilinear implicit ODEs. In
P. Deuflhard and B. Engquist (Eds.), Large–Scale Scientific Computing, pp. 37–50. Basel,
Switzerland: Birkhäuser Verlag.
Dieudonné, J. (1970). Eléments d’Analyse, Volume 3. Paris, France: Gauthier–Villars.
Doedel, E., H. B. Keller, and J. P. Kernevez (1991). Numerical analysis and control of bifurcation
problems: II Bifurcation in infinite dimensions. Int J. Bifurcation Chaos 1, 745–772.
Dolezal, V. (1964). The existence of a continuous basis of certain linear subspaces of Er which
depends on a parameter. Čas. Pro. Peˇst. Mat. 89, 466–468.
Duff, I. and C. W. Gear (1986). Computing the structural index. SIAM J. Alg. Disc. Meth. 7,
594–603.
Eich, E. (1991). Projizierende Mehrschrittverfahren zur Lösung der Bewegungsgleichungen tech-
nischer Mehrkörpersysteme mit Zwangsbedingungen und Unstetigkeiten. Ph. D. thesis, Inst.
f. Mathem., Univ. Augsburg, Augsburg, Germany.
Eich, E. (1993). Convergence results for a coordinate projection method applied to mechanical
systems with algebraic constraints. SIAM J. Numer. Anal. 30, 1467–1482.
Eich, E., C. Führer, B. Leimkuhler, and S. Reich (1990). Stabilization and projection methods
for multibody dynamics. Technical Report A281, Inst. f. Mathem., Helsinki Univ. of Techn.,
Espoo, Finland.
Eich-Soellner, E. and C. Führer (1998). Numerical Methods in Multibody Dynamics. Stuttgart,
Germany: B. G. Teubner.
Eich-Soellner, E., P. Lory, P. Burr, and A. Kroner (1997). Stationary and dynamic flowsheeting
in the chemical engineering industry. Surveys Math. Indust. 7, 1–28.
Endo, T. and L. O. Chua (1988). Chaos from phase–locked loops. IEEE Trans. Circ. and
Syst. 35, 987–1003.
Engl, G. (1996). The modeling and numerical simulation of gas flow networks. Numer. Math. 72,
349–366.
Ernsthausen, J. M. (2001). On the numerical solution of DAE–boundary value problems. Ph. D.
thesis, Dept. of Mathem., Univ. of Pittsburgh, Pittsburgh, PA. in preparation.
Fliess, M., J. Lévine, and P. Rouchon (1992). Index of a general differential–algebraic implicit
system. In S. Kimura and S. Kodama (Eds.), Recent Advances in Mathematical Theory of
Systems, Control, Network and Signal Processing I, pp. 289–294. Kobe, Japan: Mita Press.
Fliess, M., J. Lévine, and P. Rouchon (1993). Index of an implicit time–varying linear differential
equation: A noncommutative algebraic approach. Lin. Alg. and Applic. 186, 59–71.
Frank, R., F. J. Schneid, and C. W. Ueberhuber (1981). The concept of B–convergence. SIAM
J. Numer. Anal. 18, 753–780.
Frank, R., F. J. Schneid, and C. W. Ueberhuber (1985a). Order results for implicit Runge–Kutta
methods applied to stiff systems. SIAM J. Numer. Anal. 22, 515–534.

REFERENCES 344
Frank, R., F. J. Schneid, and C. W. Ueberhuber (1985b). Stability properties of implicit Runge–
Kutta methods. SIAM J. Numer. Anal. 22, 497–514.
Friedrich, K. O. (1965). Advanced Ordinary Differential Equations. New York, NY: Gordon and
Breach.
Führer, C. (1988). Differential – algebraische Gleichungssysteme in mechanischen Mehrkörper-
systemen. Ph. D. thesis, Mathem. Inst., Techn. Univ. München, München, Germany.
Führer, C. and B. J. Leimkuhler (1990). A new class of generalized inverses for the solution
of discretized Euler–Lagrange equations. In E. J. Haug and R. C. Deyo (Eds.), Real–Time
Integration Methods for Mechanical System Simulation, Volume F 69 of NATO ASI Series,
pp. 143–154. New York, NY: Springer–Verlag.
Führer, C. and B. J. Leimkuhler (1991). Numerical solution of differential–algebraic equations
for constrained mechanical motion. Numer. Math. 59, 55–69.
Gantmacher, F. R. (1953). Teorya Matrits, Vol I, II. Moscow, Russia: Gos. Izdat. Techn.-Teor.
Lit, Moscva. English translation, Chelsea Publ. Co., New York, NY, 1956.
Gärtner, W. W. (1960). Transistors: Principles, Design and Applications. Toronto, Canada:
Van Nostrand.
Gauss, K. F. (1829). Über ein neues allgemeines Grundgesetz der Mechanik. J. f. d. reine und
angew. Mathem. (Crelle) 4, 25–28.
Gear, C. W. (1971). The simultaneous numerical solution of differential–algebraic equations.
IEEE Trans. Circ. Theory CT–18, 89–95.
Gear, C. W. (1986). Maintaining solution invariants in the numerical solution of ODEs. SIAM
J. Sci. Stat. Comp. 7, 734–743.
Gear, C. W. (1988). Differential–algebraic equation index transformations. SIAM J. Sci. Stat.
Comp. 9, 39–48.
Gear, C. W. (1990). DAE indices and integral algebraic equation. SIAM J. Numer. Anal. 27,
1527–1534.
Gear, C. W., G. Gupta, and B. Leimkuhler (1985). Automatic integration of the Euler–Lagrange
equations with constraints. J. Comp. Appl. Math. 12/13, 77–90.
Gear, C. W. and L. R. Petzold (1983). Differential/algebraic systems and matrix pencils. In
B. Kagstrom and A. Ruhe (Eds.), Matrix Pencils, Volume 973 of Lect. Notes in Mathem.,
pp. 75–89. New York, NY: Springer–Verlag.
Gear, C. W. and L. R. Petzold (1984). ODE methods for the solution of differential/algebraic
systems. SIAM J. Numer. Anal. 21, 716–728.
Geerts, T. (1993). Solvability conditions, consistency and weak consistency for linear differen-
tial –algebraic equations and time–invariant singular systems: The general case. Lin. Alg.
Appl. 181, 111–130.
Goldschmidt, H. (1967a). Existence theorems for analytic linear partial differential equations.
Ann. Math. 86, 246–270.
Goldschmidt, H. (1967b). Integrability criteria for systems of non–linear partial differential
equations. J. Diff. Geom. 1, 269–307.
Golubitsky, M. and V. Guillemin (1973). Stable Mappings and their Singularities, Volume 14 of
Grad. Texts in Mathem. New York, NY: Springer–Verlag.

REFERENCES 345
Gràcia, X. and J. M. Pons (1992). A generalized geometric framework for constrained systems.
Diff. Geom. Appl. 2, 223–247.
Green, M. M. and A. N. Willson Jr. (1992). How to identify unstable dc operating points. IEEE
Trans. Circ. and Syst. 39, 820–832.
Gresho, P. M., S. T. Chan, R. L. Lee, and C. D. Upson (1984). A modified finite element method
for solving the time–dependent incompressible Navier Stokes equations. Part I: Theory. Int.
J. Num. Meth. in Fluids 4, 557–598.
Griepentrog, E. and R. März (1986). Differential–Algebraic Equations and their Numerical
Treatment, Volume 88 of Teubner Texte zur Mathem. Leipzig, Germany: B.G. Teubner
Verlag.
Griepentrog, E. and R. März (1989). Basic properties of some differential–algebraic equations.
Z. Anal. Anwend. 8, 25–40.
Griewank, A. (2000). Evaluating derivatives: Principles and Techniques of Algorithmic Differ-
entiation. Philadelphia, PA: SIAM Publications.
Griewank, A. and G. F. Corliss (Eds.) (1992). Automatic Differentiation of Algorithms. Philadel-
phia, PA: SIAM Publications.
Griewank, A. and G. W. Reddien (1983). The calculation of Hopf points by a direct method.
IMA J. Numer. Anal. 3, 295–303.
Griewank, A. and G. W. Reddien (1984). Characterization and computation of generalized
turning points. SIAM J. Numer. Anal. 21, 176–185.
Griewank, A. and G. W. Reddien (1989). Computation of cusp singularities for operator equa-
tions and their discretizations. J. Comput. Appl. Math. 26, 133–153.
Gritsis, D., C. C. Pantelides, and R. W. H. Sargent (1995). Optimal control of systems described
by index two differential–algebraic equations. SIAM J. Sci. Stat. Comp. 16, 1349–1366.
Guckenheimer, J. and M. Myers (1996). Computing Hopf bifurcations II: Three examples from
neurophysiology. SIAM J. Sci. Stat. Comp. 17, 1275–1301.
Guckenheimer, J., M. Myers, and B. Sturmfels (1997). Computing Hopf bifurcations I. SIAM
J. Numer. Anal. 34, 1–21.
Günther, M. and U. Feldmann (1999a). CAD based electric circuit modeling in industry I.
mathematical structure and index of network equations. Surv. Math. Ind. 8, 97–129.
Günther, M. and U. Feldmann (1999b). CAD based electric circuit modeling in industry II.
impact of circuit configurations and parameters. Surv. Math. Ind. 8, 131–157.
Günther, M. and M. Hoschek (1997). ROW methods adapted to electric circuit simulation
packages. Comp. and Appl. Math. 82, 159–170.
Hachtel, G. D., R. K. Brayton, and F. G. Gustavson (1971). The sparse tableau approach to
network analysis and design. IEEE Trans. Circ. Theory CT–18, 101–113.
Hairer, E. (1999). Symmetric projection methods for differential equations on manifold. preprint.
Hairer, E., C. Lubich, and M. Roche (1989). The Numerical Solution of Differential–Algebraic
Systems by Runge–Kutta Methods, Volume 1409 of Lect. Notes in Mathem. New York, NY:
Springer–Verlag.
Hairer, E., S. P. Norsett, and G. Wanner (1993). Solving Ordinary Differential Equations I:
Nonstiff Problems (2nd ed.). New York, NY: Springer–Verlag.

REFERENCES 346
Hairer, E. and G. Wanner (1996). Solving Ordinary Differential Equations II: Stiff and
Differential–Algebraic Problems (2nd ed.). New York, NY: Springer–Verlag.
Hale, J. K. (1977). Theory of Functional Differential Equations. New York, NY: Springer–Verlag.
Hall, C. A., X. Lei, and P. J. Rabier (1994). A nonstandard symmetry breaking phenomenon
in sheet metal stretching. Int. J. Engrg. Sci. 32, 1381–1397.
Hanke, M. (1988). On a least–squares collocation method for linear differential–algebraic equa-
tions. Numer. Math. 54, 79–90.
Hartman, P. (1964). Ordinary Differential Equations. New York, NY: Wiley.
Haug, E. J. (1989). Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol I.
Boston, MA: Allyn and Bacon.
Hautus, M. L. J. and L. M. Silverman (1983). System structure and singular control. Lin. Alg.
and Appl. 50, 369–402.
Hiller, M. and S. Frik (1991). Road vehicle benchmark 2: Five link suspension. In W. Kortüm,
S. Sharp, and A. de Pater (Eds.), Applications of Multibody Computer Codes to Vehicle
system dynamics. Lyon, France: IAVSD Symposium.
Hindmarsh, A. C. (1983). ODEPACK, A systematized collection of ODE solvers. In R. S.
Stepleman (Ed.), Scientific Computing, pp. 55–64. Amsterdam, The Netherlands: North–
Holland.
Holodnick, M. and M. Kubiček (1984). DERPAR–an algorithm for the continuation of periodic
solutions in ordinary differential equations. J. Comput. Phys. 55, 254–267.
Hopf, E. (1942). Abzweigung einer periodischen Lösung von einer stationären Lösung eines
Differentialsystems. Ber. der Math–Phys. Klasse der Sächsischen Akademie der Wiss. zu
Leipzig 94, 1–22.
Hoppensteadt, F. C. (1971). Properties of solutions of ordinary differential equations with small
parameters. Comm. Pure Appl. Math. 24, 807–840.
Huilgol, R. R., M. A. Janus, R.and Lohe, and T. W. Sag (1983). On the application of a
numerical algorithm for Hopf bifurcation to the hunting of a wheelset. J. Australian Math.
Soc. Ser. B 25, 384–405.
Husemoller, D. (1994). Fibre Bundles (3rd ed.). New York, NY: Springer–Verlag.
Jackson, K. R. and R. Sacks-Davis (1980). An alternative implementation of variable step–size
multistep formulas for stiff ODEs. ACM Trans. Math. Software 6, 295–318.
Jepson, A. D. (1981). Numerical Hopf bifurcation. Ph. D. thesis, Calif. Inst. of Techn., Pasadena,
CA.
Jepson, A. D. and A. Spence (1985). Folds in solutions of two parameter systems and their
calculation I. SIAM J. Numer. Anal. 22, 347–368.
Kähler, E. (1949). Einführung in die Theorie der Systeme von Differentialgleichungen,. New
York, NY: Chelsea Publ. Co.
Kalachev, L. V. and R. E. O’Malley Jr. (1995). Boundary value problems for differential alge-
braic equations. Num. Funct. Anal. and Optim. 16, 363–378.
Kampowsky, W., P. Rentrop, and W. Schmidt (1992). Classification and numerical simulation
of electrical circuits. Surv. on Math. in Industry 2, 23–65.

REFERENCES 347
Kaps, P. and P. Rentrop (1979). Generalized Runge–Kutta methods of order for with stepsize
control for stiff ordinary differential equations. Numer. Math. 33, 55–68.
Kaps, P. and G. Wanner (1981). A study of Rosenbrock–type methods of high order. Numer.
Math. 38, 279–298.
Kato, T. (1950). On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jap. 5, 435–439.
Kato, T. (1980). Perturbation Theory for Linear Operators. New York, NY: Springer–Verlag.
Kato, T. (1982). A Short Introduction to Perturbation Theory for Linear Operators. New York,
NY: Springer–Verlag.
Keller, H. B. (1992). Numerical Methods for Two Point Boundary Value Problems. New York,
NY: Dover Publ.
Kielhöfer, H. (1992). Hopf bifurcation from a differentiable viewpoint. J. Diff. Equations 97,
189–232.
Krogh, F. T. (1974). Changing step sizes in the intergation of differential equations using mod-
ified divided differences. In Proc. Conf. Numer. Sol. of ODEs, Volume 362 of Lect. Notes in
Mathem., pp. 22–71. New York, NY: Springer–Verlag.
Kronecker, L. (1890). Algebraische Reduktion der Scharen bilinearer Formen. In L. Kronecker,
Gesammelte Werke, Volume III, pp. 141–155. Berlin, Germany: Akad. d. Wiss. Berlin.
Kubiček, M. (1980). Algorithm for evaluation of complex bifurcation points in ordinary diff-
erential equations. SIAM J. Appl. Math. 38, 103–107.
Kunkel, P. and V. Mehrmann (1995). Canonical forms for linear differential–algebraic with
variable coefficients. J. Comp. Appl. Math. 56, 225–251.
Kunkel, P. and V. Mehrmann (1996). A new class of discretization methods for the solution of
linear differential–algebraic equations with variable coefficients. SIAM J. Numer. Anal. 33,
1941–1961.
Kunkel, P., V. Mehrmann, W. Rath, and J. Weickert (1997). A new software package for linear
differential algebraic equations. SIAM J. Sci. Stat. Comp. 18, 115–138.
Kuranishi, M. (1967). Lectures on Involutive Systems of Partial Differential Equations. São
Paulo, Brazil: Publ. Sociedad Mat. São Paulo.
Lagrange, J. L. (1967). Oeuvres, 14 volumes. Paris, France: Gauthier–Villars.
LakDara (1975). Singularités génériques des équations différentielles multiformes. Bol. Soc.
Brasil. Mat. 6, 95–128.
Lamour, R. (1991). Shooting methods for transferable DAEs. Numer. Math. 59, 815–829.
Lamour, R. (1997). A shooting method for fully implicit index-two differential algebraic equa-
tions. SIAM J. Sci. Stat.Comp. 18, 94–114.
Lamour, R., R. März, and R. Winkler (1998). How Floquet theory applies to index one diff-
erential algebraic equations. J. Math. Anal. Appl. 217, 372–394.
Lei, X. (1995). Singularities of a Sheet Metal Stretching Problem and Quasilinear Second Order
Ordinary Differential Equations. Ph. D. thesis, Dept. of Mathem., Univ. of Pittsburgh,
Pittsburgh, PA.
Leimkuler, B., L. R. Petzold, and C. W. Gear (1991). Approximation methods for the consistent
initialization of differential algebraic equations. SIAM J. Numer. Anal. 28, 205–226.

REFERENCES 348
Leineweber, D. B. (1996). The theory of MUSCOD in a nutshell. Technical Report IWR 96–19,
Int. Zent. f. Wiss. Rechn., Univ. Heidelberg, Heidelberg, Germany.
Leineweber, D. B. (1998). Efficient reduced SQP methods for the optimization of chemical pro-
cesses described by large sparse DAE models. Ph. D. thesis, Nat.-Math. Fakult., Univ. Hei-
delberg, Heidelberg, Germany.
Lentini, M. and R. März (1990a). The condition of boundary value problems in transferable
differential–algebraic equations. SIAM J. Numer. Anal. 27, 1001–1015.
Lentini, M. and R. März (1990b). Conditioning and dichotomy for differential algebraic equa-
tions. SIAM J. Numer. Anal. 27, 1519–1526.
LeVey, G. (1994). Differential algebraic equations, a new look at the index. Technical Report
2239, INRIA, Rennes, France.
LeVey, G. (1998). Some remarks on solvability and various indices for implicit differential equa-
tions. Numer. Algorithms 19, 127–145.
Lötstedt, P. and L. Petzold (1986a). Numerical solution of nonlinear differential equations with
algebraic constraints I: Convergence results for backward differentiation formulas. Math. of
Comp. 46, 491–516.
Lötstedt, P. and L. Petzold (1986b). Numerical solution of nonlinear differential equations with
algebraic constraints II: Practical implications. SIAM J. Sci. Stat. Comp. 7, 720–733.
Lubich, C. (1989a). h 2 –extrapolation methods for differential–algebraic systems of index two.
Impact Comp. Sci. Eng. 1, 260–268.
Lubich, C. (1989b). Linearly implicit extrapolation methods for differential–algebraic systems.
Numer. Math. 55, 197–211.
Lubich, C. (1991). Extrapolation integrators for constrained multibody systems. Impact Comp.
Sci. Eng. 3, 213–234.
Lubich, C. (1993). Integration of stiff mechanical systems by Runge–Kutta methods. ZAMP 44,
1022–1053.
Lubich, C., U. Nowak, U. Pöhle, and C. Engstler (1992). MEXX – numerical software for the
integration of constrained mechanical multibody systems. Technical Report SC 92–12, K.
Zuse Zentrum f. Inf.–technik, Berlin, Germany.
Lucht, W., K. Strehmel, and C. Eichler-Liebenow (1997a). Linear partial differential algebraic
equations, Part I: Indexes, consistent boundary/initial conditions. Technical Report 17, Inst.
f. Numer. Math., Martin Luther Univ., Halle, Germany.
Lucht, W., K. Strehmel, and C. Eichler-Liebenow (1997b). Linear partial differential algebraic
equations, Part II: Numerical solution. Technical Report 18, Inst. f Numer. Math., Martin
Luther Univ., Halle, Germany.
Mahony, R. E. and I. M. Mareels (1995). Global solutions for differential/algebraic systems and
implications for Lyapunov direct stability methods. J. Math. Syst. Estim. Control 57, 26
(electronic).
Mansfield, E. (1991). Differential Gröbner bases. Ph. D. thesis, Univ. of Sydney, Sydney, Aus-
tralia.
Marmo, G., G. Mendella, and W. M. Tulcczijew (1992). Symmetries and constant of the motion
for dynamics in implicit forms. Ann. Inst. H. Poincaré A 57, 147–166.

REFERENCES 349
Marmo, G., G. Mendella, and W. M. Tulcczijew (1995). Integrability of implicit differential
equations. J. Phys. A 28, 149–163.
Marmo, G., G. Mendella, and W. M. Tulcczijew (1997). Constrained hamiltonian systems as
implicit differential equations. J. Phys. A 30, 277–293.
Marsden, J. E. and M. F. McCracken (1976). The Hopf Bifurcation and its Applications, Vol-
ume 19 of Appl. Mathem. Sci. New York, NY: Springer–Verlag.
März, R. (1989a). Index 2 differential–algebraic equations. Results in Math. 15, 149–171.
März, R. (1989b). On boundary value problems in differential–algebraic equations. Appl. Math.
Comp. 31, 517–537.
März, R. (1989c). Some new results concerning index–3 differential–algebraic equations. J. Math.
Anal. Appl. 140, 177–199.
März, R. (1990). Higher index differential–algebraic equations: Analysis and numerical treat-
ment. In Numer. Anal. and Math. Modelling, Volume 24, pp. 199–222. Warsaw, Poland:
Banach Center.
März, R. (1992). Numerical methods for differential–algebraic equations. In A. Iserles (Ed.),
Acta Numerica 1992, pp. 141–198. Cambridge, UK: Cambridge Univ. Press.
März, R. (1994). Practical Lyapunov stability criteria for differential algebraic equations. In
Numer. Anal. and Math. Modelling, Volume 29, pp. 245–266. Warsaw, Poland: Banach
Center.
März, R. and C. Tischendorf (1994). Solving more general index–2 differential algebraic equa-
tions. Computers Math. Appl. 28, 77–105.
März, R. and E. Weinmüller (1993). Solvability of boundary value problems for systems of
singular differential–algebraic equations. SIAM J. Math. Anal. 24, 200–215.
Mattson, S. E. and G. Söderlind (1993). Index reduction in differential–algebraic equations
using dummy derivatives. SIAM J. Sci. Stat. Comp. 14, 677–692.
Medved, M. (1991). Normal forms of implicit and observed implicit differential equations. Riv.
Mat. Pura Appl. 4, 95–107.
Medved, M. (1994). Qualitative properties of generalized vector. Riv. Mat. Pura Appl. 15, 7–31.
Meerbergen, K., A. Spence, and D. Roose (1994). Shift–invert and Cayley transforms for de-
tection of rightmost eigenvalues of nonsymmetric matrices. BIT 34, 409–423.
Moore, G., T. J. Garrat, and A. Spence (1990). The numerical detection of Hopf bifurcation
points. In Continuation and Bifurcation: Numerical Techniques and Applications, NATO
ASI Series, pp. 227–259. Dordrecht, The Netherlands: Kluwer Acad. Publ.
Munthe-Kaas, H. (1999). High order Runge–Kutta methods on manifolds. Appl. Numer.
Math. 29, 115–127.
Murota, K. (1995). Structural approach in systems analysis by mixed matrices, an exposition
for index of DAEs. In K. Kirchgássner, O. Mahrenholtz, and R. Mennicken (Eds.), Proc.
ICIAM 95, pp. 257–259. Akademie Verlag.
Neimark, J. I. and N. A. Fufaev (1972). Dynamics of Nonholonomic Systems, Volume 33 of
Transl. Math. Monogr. Providencs, R.I.: Amer. Math. Society.
Neumaier, A. (1996). Molecular modeling of proteins and mathematical prediction of protein
structure. SIAM Rev. 39, 407–460.

REFERENCES 350
Nichols, N. K. (1994). Differential–algebraic equations and control system design. In Pitman
Res. Notes Math. Ser., Volume 303, pp. 208–224. Longman Sci. Tech.
Norsett, S. P. and P. Thomsen (1986). Local error control in SDIRK–methods. BIT 26, 100–113.
Oden, J. T. and J. A. C. Martins (1985). Models and computational methods for dynamic
friction phenomena. Comput. Meth. Appl. Mech. Engng. 85, 527–634.
O’Malley Jr., R. E. (1991). Singular Perturbation Methods for Ordinary Differential Equations,
Volume 89 of Appl. Mathem. Sci. New York, NY: Springer–Verlag.
Pantelides, C. C. (1988). The consistent initialization of differential–algebraic systems. SIAM
J. Sci. Stat. Comp. 9, 213–231.
Pereia, M. and J. Ambrosio (1994). Computer Aided Analysis of Rigid and Flexible Mechanical
Systems. Dordrecht, The Netherlands: Kluwer Acad. Publ.
Petzold, L. R. (1982). Differential/algebraic equations are not ODEs. SIAM J. Sci. Stat.
Comp. 3, 367–384.
Petzold, L. R. (1986). Order results for implicit Runge–Kutta methods applied to differen-
tial/algebraic systems. SIAM J. Numer. Anal. 23, 837–852.
Petzold, L. R. and F. A. Potra (1992). ODAE methods for the numerical solution of Euler–
Lagrange equations. Appl. Num. Math. 10, 397–413.
Piirilä, O.-P. and J. Tuomela (1993). Differential–algebraic systems and formal integrability.
Technical Report A326, Inst. of Mathem., Helsinki Univ. of Techn., Helsinki, Finnland.
Pommaret, J. (1978). Systems of Partial Differential Equations and Lie Pseudogroups. New
York, NY: Gordon and Breach.
Pommaret, J. (1988). Lie Pseudogroups and Mechanics. New York, NY: Gordon and Breach.
Porsching, T. A. (1985). A network model for two–fluid, two–phase flow. Num. Meth. Partial
Diff. Equ. 1, 295–313.
Potra, F. A. (1993). Implementation of linear multistep methods for solving constrained equa-
tions of motion. SIAM J. Numer. Anal. 30, 774–789.
Potra, F. A. and W. C. Rheinboldt (1989). Differential–geometric techniques for solving
differential–algebraic equations. In E. Haug and R. Deyo (Eds.), Real–Time Integration
Methods for Mech. System Simulation, Volume F 69 of NATO ASI Series, pp. 155–191.
New York, NY: Springer–Verlag.
Potra, F. A. and W. C. Rheinboldt (1991). On the numerical solution of the Euler–Lagrange
equations. Mech. Struct. and Mach. 19, 1–18.
Powell, M. J. D. (1978). A fast algorithm for nonlinearly constrained optimization calculations.
In G. A. Watson (Ed.), Numerical Analysis, Dundee 1977, Volume 630 of Lect. Notes in
Math., pp. 144–157. Berlin, Germany: Springer–Verlag.
Prothero, A. and A. Robinson (1974). On the stability and accuracy of one–step methods for
solving stiff systems of ordinary differential equations. Math. of Comp. 28, 145–162.
Quéré, M.-P. (1994). Une forme normale pour les daes linéaires. Technical Report RT 122,
LMC–IMAG, Grenoble, France.
Quillen, D. (1964). Formal properties of overdetermined systems of linear partial differential
equations. Ph. D. thesis, Harvard Univ., Cambridge, MA.

REFERENCES 351
Rabier, P. J. (1989). Implicit differential equations near a singular point. J. Math. Anal.
Appl. 144, 425–449.
Rabier, P. J. (1999). The Hopf bifurcation theorem for quasilinear differential–algebraic equa-
tions. Comp. Meth. Appl. Mech. Engrg. 170, 355–371.
Rabier, P. J. and G. W. Reddien (1986). Characterization and computation of singular points
with maximum rank deficiency. SIAM J. Numer. Anal. 23, 1040–1051.
Rabier, P. J. and W. C. Rheinboldt (1990). On a computational method for the second funda-
mental tensor and its application to bifurcation problems. Numer. Math. 57, 681–694.
Rabier, P. J. and W. C. Rheinboldt (1991). A general existence and uniqueness theory for
implicit differential–algebraic equations. Diff. and Integral Equations 4, 563–582.
Rabier, P. J. and W. C. Rheinboldt (1994a). Finite difference methods for time–dependent,
linear differential algebraic equations. Appl. Math. Letters 7, 29–34.
Rabier, P. J. and W. C. Rheinboldt (1994b). A geometric treatment of implicit differential–
algebraic equations. J. Diff. Equations 109, 110–146.
Rabier, P. J. and W. C. Rheinboldt (1994c). On impasse points of quasilinear differential–
algebraic equations. J. Math. Anal. Appl. 181, 429–454.
Rabier, P. J. and W. C. Rheinboldt (1994d). On the computation of impasse points of quasilinear
differential–algebraic equations. Math. of Comp. 62, 133–154.
Rabier, P. J. and W. C. Rheinboldt (1995). On the numerical solution of the Euler–Lagrange
equations. SIAM J. Numer. Anal. 32, 318–329.
Rabier, P. J. and W. C. Rheinboldt (1996a). Classical and generalized solutions of time–
dependent linear DAEs. Lin. Alg. Appl. 245, 259–293.
Rabier, P. J. and W. C. Rheinboldt (1996b). Discontinuous solutions of semilinear differential–
algebraic equations. Part I: Distribution solutions. Nonlin. Anal.: Theory, Meth., Applic. 27,
1241–1256.
Rabier, P. J. and W. C. Rheinboldt (1996c). Discontinuous solutions of semilinear differential–
algebraic equations. Part II: P–consistency. Nonlin. Anal.: Theory, Meth., Applic. 27, 1257–
1280.
Rabier, P. J. and W. C. Rheinboldt (1996d). Time–dependent linear DAEs with discontinuous
inputs. Lin. Alg. Appl. 247, 1–29.
Rabier, P. J. and W. C. Rheinboldt (2000). Nonholonomic Motion of Rigid Mechanical Systems
from a DAE Viewpoint. Philadelphia, PA: SIAM Publications.
Rath, W. (1995). Canonical forms for linear descriptor systems with variable coefficients. Tech-
nical Report SPC 95–16, Sci. Parall. Comp., Techn. Univ. Chemnitz–Zwickau, Chemnitz,
Germany.
Reich, S. (1989). Beitrag zur Theorie der Algebrodifferentialgleichungen. Ph. D. thesis, Fakult.
Elektrotech., Univ. Dresden, Dresden, Germany.
Reich, S. (1990a). On a geometric characterization of differential–algebraic equations. Math.
Res. 59, 105–113.
Reich, S. (1990b). On a geometric interpretation of differential–algebraic equations. Circ. Syst.
Signal Process. 9, 367–382.

REFERENCES 352
Reich, S. (1991). On an existence and uniqueness theory for nonlinear differential–algebraic
equations. Circ. Syst. Signal Process. 10, 343–359. Erratum ibid. 11, 1992.
Reiszig, G. (1996). Differential–algebraic equations and impasse points. IEEE Trans. Circ. and
Syst. 43, 122–133.
Reiszig, G. (1997). Beiträge zu Theorie and Anwendungen von Differentialgleichungen. Ph. D.
thesis, Fakult. Elektrotech., Univ. Dresden, Dresden, Germany.
Reiszig, G. and H. Boche (1998). Singularities of implicit ordinary differential equations. In
Proc. 1998 ISCAS.
Rentrop, P., M. Roche, and G. Steinebach (1989). The application of Rosenbrock–Wanner type
methods with stepsize control in differential–algebraic equations. Numer. Math. 55, 545–563.
Rheinboldt, W. C. (1988). On the computation of multi–dimensional solution manifolds of
parametrized equations. Numer. Math. 53, 165–181.
Rheinboldt, W. C. (1996). MANPACK: A set of algorithms for computations on implicitly
defined manifolds. Comp. Math. w. Appl. 27, 15–28.
Rheinboldt, W. C. (1997). Solving algebraically explicit DAEs with the MANPACK manifold
algorithms. Comp. Math. w. Appl. 27, 31–43.
Rheinboldt, W. C. and B. Simeon (1995). Performance analysis of some methods for solving
Euler Lagrange equations. Appl. Math. Letters 8, 77–82.
Rheinboldt, W. C. and B. Simeon (1999). Computing smooth solutions of DAEs for elastic
multibody systems. Comp. Math. w. Appl. 37, 69–83.
Riaza, R. and P. J. Zufiria (1999). Stability of singular equilibria in linearly implicit differential
equations. preprint.
Riquier, C. (1910). Les Systèmes d’Equations aux Dérivées Partielles. Paris, France: Gauthiers–
Villars.
Roche, M. (1988). Rosenbrock methods for differential–algebraic systems. Numer. Math. 52,
45–63.
Roose, D. and V. Hlavaček (1985). A direct method for the computation of Hopf bifurcation
points. SIAM J. Appl. Math. 45, 879–894.
Rosenbrock, H. H. (1962/63). Some general implicit processes for the numerical solution of
differential equations. Computer J. 5, 329–330.
Rulka, W. (1989). SIMPACK, Ein Rechenprogram zur Simulation von Mehrkörpersystemen mit
grossen Bewegungen. In Proc. Finite Elem. der Praxis, Computergestütztes Berechnen und
Konstruieren, pp. 206–245. Reutlingen, Germany: T–PROGRAMM GMBH.
Sastry, S. S. and C. A. Desoer (1981). Jump behavior of circuits and systems. IEEE Trans.
Circ. and Syst. 28, 1109–1124.
Sattinger, D. H. (1973). Topics in Stability and Bifurcation Theory, Volume 309 of Lect. Notes
Math. New York, NY: Springer–Verlag.
Schulz, V. (1996). Reduced SQP methods for large–scale optimal control problems in DAE with
application to path planning problems for satellite mounted robots. Ph. D. thesis, Nat.-Math.
Fakult., Univ. Heidelberg, Heidelberg, Germany.

REFERENCES 353
Schulz, V. H., H. G. Bock, and M. C. Steinbach (1998). Exploiting invariants in the numerical
solution of multipoint boundary value problems for DAEs. SIAM J. Numer. Anal. 19, 440–
487.
Schwartz, L. (1966). Théorie des Distributions. Paris, France: Hermann.
Seshu, S. and H. Reed (1961). Linear Graphs and Electrical Networks. Reading, MA: Addison–
Wesley Publ. Co.
Shampine, L. F. (1986). Conservation laws and the numerical solution of ODEs. Comp. and
Math. w. Appl. Part B 12, 1287–1296.
Shampine, L. F. and M. K. Gordon (1975). Computer Solution of Ordinary Differential Equa-
tions. San Francisco, CA: W. H. Freeman and Co.
Silverman, L. M. and R. S. Bucy (1970). Generalizations of a theorem of Dolezal. Math. Syst.
Theory 4, 334–339.
Simeon, B. (1994). Numerische Integration mechanischer Mehrkörpersysteme: Algorithmen und
Rechenprogramme. Ph. D. thesis, Mathem. Inst., Techn. Univ. München, München, Ger-
many.
Simeon, B. (1996). Modelling a flexible slider crank mechanism by a mixed system of DAEs and
PDEs. Mathem. Modelling of Syst. 2, 1–18.
Simeon, B. (1999). Numerische Simulation gekoppelter Systeme von partiellen und differential–
algebraischen Gleichungen in der Mehrkörperdynamik. Habilitationsschrift, Math. Fakult.,
Univ. Karlsruhe, Karlsruhe, Germany.
Simeon, B., C. Führer, and P. Rentrop (1991). Differential–algebraic equations in vehicle system
dynamics. Surv. Math. Ind. 1, 1–37.
Simeon, B., C. Führer, and P. Rentrop (1993). The Drazin inverse in multibody system dynam-
ics. Numer. Math. 64, 521–539.
Simeon, B., F. Grupp, C. Führer, and P. Rentrop (1992). A nonlinear truck model and its
treatment as a multibody system. Technical Report TUM–M9204, Math. Inst., Tech. Univ
München, München, Germany.
Sincovec, R. F., A. M. Erisman, E. L. Yip, and M. A. Epton (1981). Analysis of descriptor
systems using numerical algorithms. IEEE Trans. Autom. Contr. AC–26, 139–147.
Slepian, P. (1968). Mathematical Foundations of Network Analysis, Volume 16 of Tracts in Nat.
Philos. New York, NY: Springer–Verlag.
Smale, S. (1972). On the mathematical foundation of electrical networks. J. Diff. Geom. 1,
193–210.
Spencer, D. (1969). Overdetermined systems of linear partial differential equations. Bull. Am.
Math. Soc. 75, 179–239.
Spivak, M. (1979). A Comprehensive Introduction to Differential Geometry, Five Volumes (2nd
ed.). Berkeley, CA: Publish or Perish, Inc.
Steenrod, N. (1951). The Topology of Fibre Bundles. Princeton, NJ: Princeton Univ. Press.
Szatkowski, A. (1992). Geometric characterization of singular differential algebraic equations.
Int. J. Syst. Sci. 23, 167–186.

REFERENCES 354
Takens, F. (1976). Constrained equations: A study of implicit differential equations and their
discontinuous solutions. In Lecture Notes in Math., Volume 525, pp. 143–234. New York,
NY: Springer–Verlag.
Thom, R. (1972). Sur les équations différentielles multiformes et leurs intégrales singulières.
Bol. Soc. Brasil. Mat. 3, 1–11.
Thomas, G. (1995a). Algebraic approach for quasi–linear differential algebraic equations. Tech-
nical Report RT 135, LMC–IMAG, Grenoble, France.
Thomas, G. (1995b). Symbolic computation of the index of quasilinear differential–algebraic
equations. Technical Report preprint, LMC–IMAG, Grenoble, France.
Thomas, G. (1997). The problem of defining the singular points of quasi–linear differential–
algebraic systems. Theoret. Comput. Sci. 187, 49–79.
Thompson, J. M. T. and H. B. Stewart (1986). Nonlinear Dynamics and Chaos. Chichester,
UK: J. Wiley.
Tischendorf, C. (1995). Feasibility and stability behaviour of the BDF applied to index–2
differential–algebraic equations. Z. Angew. Math. Mech. 75, 927–946.
Topunov, V. (1989). Reducing systems of partial differential equations to a passive form.
In A. M. Vinogradov (Ed.), Symmetries of partial differential equations. Dordrecht, The
Netherlands: Kluwer Acad. Publ.
Trajkovic, I. and A. N. Willson Jr. (1988). Behavior of nonlinear transistor one–ports: Things
are not always as simple as might be expected. In Proc. 30th Midwest Symposium on Circuits,
Syracuse, NY.
Tuomela, J. (1997). On singular points of quasilinear differential and differential–algebraic equa-
tions. BIT 37, 968–977.
Venkatasubramanian, V. (1994). Singularity induced bifurcation in the Van der Pol oscillator.
IEEE Trans. Circ. and Syst. 41, 765–769.
Venkatasubramanian, V., H. Schättler, and J. Zaborsky (1991). A taxonomy of the dynamics of
the large power system with emphasis on its voltage stability. In Proc. NSF Int. Workshop
on Bulk Power System Voltage phenomena– II, pp. 9–52.
Verghese, G. C., B. C. Levy, and T. Kailath (1981). A generalized state-space for singular
systems. IEEE Trans. Autom. Contr. AC–26, 811–831.
vonSchwerin, R. (1995). Numerical Methods, Algorithms, and Software for Higher Index Non-
linear Differential–Algebraic Equations in Multibody System Simulation. Ph. D. thesis, Nat.-
Math. Fakult., Univ. of Heidelberg, Heidelberg, Germany.
vonSosen, H. (1994). Folds and bifurcations in the solutions of semi–explicit differential–algebraic
equations. Ph. D. thesis, Calif. Inst. of Techn., Pasadena, CA.
Wehage, R. A. and E. J. Haug (1982). Generalized coordinate partitioning for dimension reduc-
tion in analysis of constrained dynamic systems. J. Mech. Design 104, 247–255.
Weierstrass, K. (1868). Zur Theorie der bilinearen und quadratischen Formen. In K. Weier-
strass, Gesammelte Werke, Bd. II,, pp. 19–44. Berlin, Germany: Akad. d. Wiss. Berlin.
Winkler, R. (1994). On simple impasse points and their numerical computation. Technical
Report 94–15, Inst. f. Mathem., Humboldt Univ. zu Berlin, Berlin, Germany.

REFERENCES 355
Wosle, M. and F. Pfeiffer (1996). Dynamics of multibody systems containing dependent unilat-
eral constraints with friction. J. Vibration and Control 2, 161–192.
Wulff, C., A. Hohman, and P. Deuflhard (1994). Numerical continuation of periodic orbits with
symmetry. Technical Report SC 94–12, K. Zuse Zentrum f. Inf.–technik, Berlin, Germany.
Yan, X. (1993). Singularly perturbed differential algebraic equations. Ph. D. thesis, Dept. of
Mathem., Univ. of Pittsburgh, Pittsburgh, PA.
Yen, J. (1993). Constrained equations of motion in multibody dynamics as ODEs on manifolds.
SIAM J. Numer. Anal. 30, 553–568.
Zeidler, E. (1989). Nonlinear Functional Analysis and its Applications, Vol III. New York, NY:
Springer–Verlag.
Zheng, Q. (1990). Hopf bifurcation in differential–algebraic equations and applications to circuit
simulations. Int. Series Num. Math. 93, 45–58.
Zheng, Q. and R. Neubert (1997). Computation of periodic solutions of differential-algebraic
equations in the neighborhood of Hopf bifurcation points. Int. J. Bifurcation Chaos 7, 2773–
2787.
Ziesse, M. W., H. G. Bock, J. V. Galitzendoerfer, and J. P. Schloeder (1996). Parameter estima-
tion in multispecies transport reaction systems using parallel algorithms. In J. Gottlieb and
P. DuChateau (Eds.), Parameter Identification and Inverse Problems in Hydrology, Geology,
and Ecology, pp. 273–282. Dordrecht, The Netherlands: Kluwer Acad. Publ.