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