Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

BIT Numerical Mathematics

Volumn 38, Issue 2, 1998, Pages 391-414

  Schmitt, Bernhard A ^a   Weiner, Rüdiger ^b  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

Equilibrium attractivity; Krylov methods; Stiff ODEs; W methods

Indexed keywords

EID: 0007111726     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02512374     Document Type: Article

References (17)

1. P. N. Brown and A. C. Hindmarsh, Matrix-free methods for stiff systems of ODEs. SIAM J. Numer. Anal., 23 (1986), pp. 610-638.
2. M. Büttner, B. A. Schmitt, and R. Weiner, W-methods with automatic partitioning by Krylov techniques for large stiff systems, SIAM J. Numer. Anal., 32 (1995), pp. 260-284.
3. R. Frank, J. Schneid, and C. W. Ueberhuber, The concept of B-convergence, SIAM J. Numer. Anal., 18 (1981), pp. 753-780.
4. E. Gallopoulos and Y. Saad, Efficient solution of parabolic equations by Krylov approximation methods, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 1236-1264.
5. E. Hairer, G. Bader, and Ch. Lubich, On the stability of semi-implicit methods for ordinary differential equations, BIT, 22 (1982), pp. 211-232.
6. M. Hochbruck, C. Lubich, and H. Selhofer, Exponential integrators for large systems of differential equations, to appear in SIAM J. Sci. Comput.
7. P. Kaps and P. Rentrop, Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations, Numer. Math., 38 (1981), pp. 279-298.
8. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
9. Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems, Math. Comp., 37 (1981), pp. 105-126.
10. Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual method for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
11. Y. Saad, On the Lanczos method for solving symmetric linear systems with several right hand sides, Math. Comp., 48 (1987), pp. 651-662.
12. B. A. Schmitt, Norm bounds for rational matrix functions, Numer. Math., 42 (1983), pp. 379-389.
13. B. A. Schmitt and R. Weiner, Matrix-free W-methods using a multiple Arnoldi iteration, Appl. Numer. Math., 18 (1995), pp. 307-320.
14. T. Steihaug and A. Wolfbrandt, An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff ordinary differential equations, Math. Comp., 33 (1979), pp. 521-534.
15. A. M. Stuart and A. R. Humphries, Model problems in numerical stability theory for initial value problems, SIAM Review, 36 (1994), pp. 226-257.
16. R. Weiner and B. A. Schmitt, Consistency of Krylov- W-methods in initial value problems, Report 14, Fachbereich Mathematik und Informatik, University of Halle, 1995.
17. R. Weiner, B. A. Schmitt, and H. Podhaisky, ROWMAP - a ROW-code with Krylov techniques for large stiff ODEs, Appl. Numer. Math., 25 (1997), pp. 303-319.