Linearly-implicit two-step methods and their implementation in Nordsieck form

Applied Numerical Mathematics

Volumn 56, Issue 3-4 SPEC. ISS., 2006, Pages 374-387

  Podhaisky, H ^a   Weiner, R ^a   Schmitt, B A ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

General linear methods; Linearly implicit two step methods; Nordsieck representation; Peer method

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

GENERAL LINEAR METHODS; LINEARLY-IMPLICIT TWO-STEP METHODS; NORDSIECK REPRESENTATION; PEER-METHOD;

LINEAR EQUATIONS;

EID: 33644617899     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2005.04.024     Document Type: Article

References (13)

1. J.C. Butcher Numerical Methods for Ordinary Differential Equations 2003 Wiley New York
2. J.C. Butcher, H. Podhaisky, On error estimation in general linear methods for stiff ODEs, Appl. Numer. Math., in press
3. J.C. Butcher, and Z. Jackiewicz Unconditionally stable general linear methods for ordinary differential equations BIT 44 2004 557 570
4. E. Hairer, and G. Wanner Solving Ordinary Differential Equations II 1996 Springer Berlin
5. Z. Jackiewicz, H. Podhaisky, and R. Weiner Construction of highly stable two-step W-methods for ordinary differential equations J. Comput. Appl. Math. 167 2004 389 403
6. H.O. Kreiss Difference methods for stiff ordinary differential equations SIAM J. Numer. Anal. 15 1978 21 58
7. H. Podhaisky, B.A. Schmitt, and R. Weiner Design, analysis and testing of some parallel two-step W-methods for stiff systems Appl. Numer. Math. 42 2002 381 395
8. H. Podhaisky, R. Weiner, and B.A. Schmitt Two-step W-methods for stiff ODE systems Vietnam J. Math. 30 2002 591 603
9. H. Podhaisky, R. Weiner, and B.A. Schmitt Rosenbrock-type 'Peer' two-step methods Appl. Numer. Math. 53 2005 409 420
10. B.A. Schmitt, and R. Weiner Parallel two-step W-methods with Peer variables SIAM J. Numer. Anal. 42 2004 265 282
11. B.A. Schmitt, R. Weiner, and K. Erdmann Implicit parallel Peer methods for stiff initial value problems Appl. Numer. Math. 53 2005 457 470
12. R. Weiner, B.A. Schmitt, and H. Podhaisky ROWMAP - a ROW-code with Krylov techniques for large stiff ODEs Appl. Numer. Math. 25 1997 303 319
13. R. Weiner, B.A. Schmitt, and H. Podhaisky Parallel 'Peer' two-step W-methods and their application to MOL systems Appl. Numer. Math. 48 2004 425 439