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