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