A new class of discretization methods for the solution of linear differential-algebraic equations with variable coefficients

SIAM Journal on Numerical Analysis

Volumn 33, Issue 5, 1996, Pages 1941-1961

  Kunkel, Peter ^a   Mehrmann, Volker ^b  

^a UNIVERSITY OF OLDENBURG   (Germany)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Backward difference formulas; Canonical forms; Differential algebraic equations; Least squares regularization; Singular pencils; Strangeness index

Indexed keywords

EID: 0000363441     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994240364     Document Type: Article

References (31)

1. A. BARRLUND, Constrained least squares methods for linear timevarying DAE systems, Numer. Math., 60 (1991), pp. 145-161.
2. K. BRENAN, S. CAMPBELL, AND L. PETZOLD, Numerical Solution of Initial-Value Problems in Differential Algebraic Equations, Elsevier-North Holland, New York, 1989.
3. S. L. CAMPBELL, A general form for solvable linear time varying singular systems of differential equations, SIAM J. Math. Anal., 18 (1987), pp. 1101-1114.
4. _, Local realizations of time varying descriptor systems, in Proceedings of the 26th IEEE Conference on Decision and Control, 1987, pp. 1129-1130.
5. _, The numerical solution of higher index linear time varying singular systems of differential equations, SIAM J. Sci. Statist. Comput., 6 (1988), pp. 334-348.
6. _, Uniqueness of completions for linear time varying differential algebraic equations, Linear Algebra Appl., 161 (1992), pp. 55-67.
7. S. L. CAMPBELL AND E. GRIPENTROG, Solvability of general differential algebraic equations, SIAM J. Sci. Comput., 16 (1995), pp. 257-270.
8. S. L. CAMPBELL AND E. MOORE, Progress on a General Numerical Method for Nonlinear Higher Index DAEs, Circuits Systems Signal Process., 13 (1994), pp. 123-128.
9. _, Constraint Preserving Integrators for General Nonlinear Higher Index DAEs, Numer. Math., 69 (1994), pp. 383-399.
10. P. DEUFLHARD, E. HAIRER, AND J. ZUGCK, One-step and extrapolation methods for differential-algebraic systems, Numer. Math., 51 (1987), pp. 501-516.
11. C. FÜHRER, Differential-Algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen, Dissertation, Technische Universität München, München, 1988.
12. C. FÜHRER AND B. J. LEIMKUHLER, Numerical solution of differential-algebraic equations for constrained mechanical motion, Numer. Math., 59 (1991), pp. 55-69.
13. C. W. GEAR, Differential-algebraic index transformations, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 39-47.
14. C. W. GEAR AND L. R. PETZOLD, Differential-algebraic systems and matrix pencils, in Matrix Pencils, B. Kågstrom and A. Ruhe, eds., Springer-Verlag, Berlin, 1983, pp. 75-90.
15. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
16. E. GRIEPENTROG AND R. MÄRZ, Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Verlag, Leipzig, 1986.
17. E. HAIRER, C. LUBICH, AND M. ROCHE, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Springer-Verlag, Berlin, 1989.
18. E. HAIRER, S. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations I, Springer-Verlag, Berlin, 1987.
19. E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II, Springer-Verlag, Berlin, 1991.
20. B. HANSEN, Comparing Different Concepts to Treat Differential-Algebraic Equations, Tech. report 220, Sektion Mathematik, Humboldt Universität Berlin, Berlin, 1989.
21. P. KUNKEL AND V. MEHRMANN, Numerical solution of differential-algebraic Riccati equations, Linear Algebra Appl., 137/138 (1990), pp. 39-66.
22. _, Smooth factorizations of matrix valued functions and their derivatives, Numer. Math., 60 (1991), pp. 115-132.
23. _, Canonical forms for linear differential-algebraic equations with variable coefficients, J. Comput. Appl. Math., 56 (1994), pp. 225-251.
24. C. LUBICH, U. NOWAK, U. PÖLE, AND C. ENGSTLER, MEXX - Numerical Software for the Integration of Constrained Mechanical Multibody Systems, Tech. report SC 92-12, ZIB, Berlin, 1992.
25. R. MÄRZ, Numerical Methods for Differential-Algebraic Equations I: Characterizing DAEs, Tech. report 91-32/I, Fachbereich Mathematik, Humboldt Universität Berlin, Berlin, 1991.
26. _, Numerical Methods for Differential-Algebraic Equations II: Numerical Integration Methods, Tech. report 91-32/II, Fachbereich Mathematik, Humboldt Universität Berlin, Berlin, 1991.
27. V. MEHRMANN, The Autonomous Linear Quadratic Control Problem, Springer-Verlag, Berlin, 1991.
28. L. R. PETZOLD, A description of DASSL: A differential/algebraic systems solver, in Scientific Computing, R. S. Stepleman et al., ed., North-Holland, Amsterdam, 1983, pp. 65-68.
29. P. RABIER AND W. RHEINBOLDT, Classical and Generalized Solutions of Time-Dependent Linear Differential Algebraic Equations, Tech. report, Dept. of Mathematics and Statistics, Univ. of Pittsburgh, Pittsburgh, PA, 1993, Linear Algebra Appl., to appear, 1996.
30. B. SIMEON, F. GRUPP, C. FÜHRER, AND P. RENTROP, A nonlinear truck model and its treatment as a multibody system, J. Comput. Appl. Math., 50 (1994), pp. 523-532.
31. T. SCHMIDT AND M. HOU, Rollringgetriebe, Internal report, Sicherheitstechnische Regelungs- und Meßtechnik, Bergische Universität, GH Wuppertal, Wuppertal, FRG, 1992.