Construction of highly stable two-step W-methods for ordinary differential equations

Journal of Computational and Applied Mathematics

Volumn 167, Issue 2, 2004, Pages 389-403

  Jackiewicz, Z ^a   Podhaisky, H ^b   Weiner, R ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

A stability; L stability; Stiff differential systems; Two step W methods

Indexed keywords

COMPUTATIONAL METHODS; CONSTRUCTION; CONVERGENCE OF NUMERICAL METHODS;

NUMERICAL SOLUTION; STEPSIZE PATTERN; STIFF DIFFERENTIAL SYSTEMS; TWO-STEP W-METHODS;

DIFFERENTIAL EQUATIONS;

MATHEMATICAL ANALYSIS;

EID: 2442573699     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.10.007     Document Type: Article

References (20)

1. Bartoszewski Z. Jackiewicz Z. Construction of two-step Runge-Kutta methods of high order for ordinary differential equations Numer. Algorithms 18 1998 51-70
2. Butcher J.C. General linear methods for stiff differential equations BIT 41 2001 240-264
3. Butcher J.C. Jackiewicz Z. Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations Appl. Numer. Math. 21 1996 385-415
4. Butcher J.C. Jackiewicz Z. Construction of high order diagonally implicit multistage integration methods for ordinary differential equations Appl. Numer. Math. 27 1998 1-12
5. Butcher J.C. Jackiewicz Z. Mittelmann H.D. A nonlinear optimization approach to the construction of general linear methods of high order J. Comput. Appl. Math. 81 1997 181-196
6. Guglielmi N. Zennaro M. On the asymptotic properties of a family of matrices Linear Algebra Appl. 322 2001 169-192
7. Guglielmi N. Zennaro M. On the zero-stability of variable step-size multistep methods: the spectral radius approach Numer. Math. 88 2001 445-458
8. Hairer E. Wanner G. Solving Ordinary Differential Equations II. Stiff and Diffferential-Algebraic Problems 1996 Springer Berlin, Heidelberg, New York
9. Hochbruck M. Lubich Ch. Selhofer H. Exponential integrators for large systems of differential equations SIAM J. Sci. Comput. 19 1998 1552-1574
10. Z. Jackiewicz, Error estimation and control for two-step W-methods, in preparation.
11. Jackiewicz Z. Mittelmann H.D. Exploiting structure in the construction of DIMSIMs J. Comput. Appl. Math. 107 1999 233-239
12. Jackiewicz Z. Tracogna S. A general class of two-step Runge-Kutta methods for ordinary differential equations SIAM J. Numer. Anal. 32 1995 1390-1427
13. Kaps P. Rentrop P. Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations Numer. Math. 38 1979 55-68
14. Kreiss H.O. Difference methods for stiff ordinary differential equations SIAM J. Numer. Anal. 15 1978 21-58
15. Lambert J.D. Computational Methods in Ordinary Differential Equations 1973 Wiley Chichester, New York
16. H. Podhaisky, Parallele Zweischritt-W-Methoden, Ph.D. Thesis, Martin-Luther-Universität, Halle-Wittenberg, 2002.
17. H. Podhaisky, B.A. Schmitt, R. Weiner, Two-step W-methods with parallel stages, Report 22, Institute of Numerical Mathematics, Martin-Luther-Universität, Halle-Wittenberg, 1999.
18. Podhaisky H. Schmitt B.A. Weiner R. Design, analysis and testing of some parallel two-step W-methods for stiff systems Appl. Numer. Math. 42 2002 381-395
19. Schmitt B.A. Weiner R. Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs BIT 38 1998 391-414
20. Weiner R. Schmitt B.A. Podhaisky H. Two-step W-methods on singular perturbation problems Wyrzykowski R., et-al. PPAM 2001 Lecture Notes in Computer Science Vol. 2328 2002 778-785 Springer Berlin