Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index

BIT Numerical Mathematics

Volumn 38, Issue 3, 1998, Pages 415-438

  Arnold, M ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

Differential algebraic systems; Explicit Runge Kutta methods; Half explicit methods

Indexed keywords

EID: 0346552885     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510252     Document Type: Article

References (20)

1. M. Arnold, Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiell-algebraische Systeme von höherem Index, Habilitationsschrift, Universität Rostock, Mathematisch-Naturwissenschaftliche Fakultät, Dezember 1996.
2. U. Ascher and P. Lin, Sequential regularization methods for higher index DAEs with constraint singularities. The linear index-2 case, SIAM J. Numer. Anal., 33 (1996), pp. 1921-1940.
3. V. Brasey, A half-explicit method of order 5 for solving constrained mechanical systems, Computing, 48 (1992), pp. 191-201.
4. V. Brasey and E. Hairer, Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, SIAM J. Numer. Anal., 30 (1993), pp. 538-552.
5. V. Brasey and E. Hairer, Symmetrized half-explicit methods for constrained mechanical systems, Appl. Numer. Math., 13 (1993), pp. 23-31.
6. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, 2nd ed., 1996.
7. J. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods, Wiley, Chichester, 1987.
8. J. Dormand and P. Prince, A family of embedded Runge-Kutta formulae, J. Comp. Appl. Math., 6 (1980), pp. 19-26.
9. C. Gear, B. Leimkuhler, and G. Gupta, Automatic integration of Euler-Lagrange equations with constraints, J. Comp. Appl. Math., 12&13 (1985), pp. 77-90.
10. E. Hairer, C. Lubich, and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, 1409, Springer-Verlag, Berlin, 1989.
11. E. Hairer, S. Nørsett, and G. Wanner, Solving Ordinary Differential Equations. I. Nonstiff Problems, Springer-Verlag, Berlin, 2nd ed., 1993.
12. E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin Heidelberg New York, 2nd ed., 1996.
13. 2-extrapolation methods for differential-algebraic systems of index 2, Impact Comput. Sc. Eng., 1 (1989), pp. 260-268.
14. C. Lubich and M. Roche, Rosenbrock methods for differential-algebraic systems with solution dependent singular matrix multiplying the derivative, Computing, 43 (1990), pp. 325-342.
15. A. Murua, Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, Computing, 59 (1997), pp. 43-61.
16. J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
17. A. Ostermann, A class of half-explicit Runge-Kutta methods for differential-algebraic systems of index 3, Appl. Numer. Math., 13 (1993), pp. 165-179.
18. B. Simeon, MBSPACK - Numerical integration software for constrained mechanical motion, Surveys on Mathematics for Industry, 5 (1995), pp. 169-202.
19. B. Simeon, On the numerical solution of a wheel suspension benchmark problem, Comp. Appl. Math., 66 (1996), pp. 443-456.
20. S. Wolfram, Mathematica. A System for Doing Mathematics by Computer, Addison-Wesley, Redwood City, 2nd ed., 1991.