Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas
作者： Per Lotstedt , Linda Petzold
DOI: 10.2307/2007989
关键词:
摘要: In this paper we investigate the behavior of numerical ODE methods for solution systems differential equations coupled with algebraic constraints. Systems form arise frequently in modelling problems from physics and engineering; study some particular examples electrical networks, fluid dynamics constrained mechanical systems. We show that backward differentiation formulas converge expected order accuracy these
ams.org
osti.gov
jstor.org
sci-hub.se 参考文章(24)
FRANKLIN H. BRANIN, THE NETWORK CONCEPT AS A UNIFYING PRINCIPLE IN ENGINEERING AND THE PHYSICAL SCIENCES Problem Analysis in Science and Engineering. pp. 41- 111 ,(1977) , 10.1016/B978-0-12-125550-3.50007-7
Kathryn Eleda Brenan, Stability and convergence of difference approximations for higher index differential-algebraic systems with applications in trajectory control U.M.I.. ,(1983)
Richard Courant, K. O. Friedrichs, Supersonic flow and shock waves ,(1948)
Donald Albert Calahan, Computer Aided Network Design ,(1972)
B. Paul, Analytical dynamics of mechanisms—a computer oriented overview Mechanism and Machine Theory. ,vol. 10, pp. 481- 507 ,(1975) , 10.1016/0094-114X(75)90005-1
Stephen L. Campbell, The Numerical Solution of Higher Index Linear Time Varying Singular Systems of Differential Equations SIAM Journal on Scientific and Statistical Computing. ,vol. 6, pp. 334- 348 ,(1985) , 10.1137/0906024
Stephen L. Campbell, Linda R. Petzold, CANONICAL FORMS AND SOLVABLE SINGULAR SYSTEMS OF DIFFERENTIAL EQUATIONS Siam Journal on Algebraic and Discrete Methods. ,vol. 4, pp. 517- 521 ,(1983) , 10.1137/0604051
Linda Petzold, Per Lötstedt, Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints II: Practical Implications SIAM Journal on Scientific and Statistical Computing. ,vol. 7, pp. 720- 733 ,(1986) , 10.1137/0907049
Per Lötstedt, Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints Siam Journal on Applied Mathematics. ,vol. 42, pp. 281- 296 ,(1982) , 10.1137/0142022
E.S. Kuh, R.A. Rohrer, The state-variable approach to network analysis Proceedings of the IEEE. ,vol. 53, pp. 672- 686 ,(1965) , 10.1109/PROC.1965.3991