Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Design, analysis and testing of some parallel two-step W-methods for stiff systems
Applied Numerical Mathematics
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Parallel 'Peer' two-step W-methods and their application to MOL-systems
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Construction of highly stable two-step W-methods for ordinary differential equations
Journal of Computational and Applied Mathematics
Explicit two-step peer methods
Computers & Mathematics with Applications
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
High-order linearly implicit two-step peer -- finite element methods for time-dependent PDEs
Applied Numerical Mathematics
Parameter optimization for explicit parallel peer two-step methods
Applied Numerical Mathematics
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It is well known that one-step Rosenbrock methods may suffer from order reduction for very stiff problems. By considering two-step methods we construct s-stage methods where all stage values have stage order s-1. The proposed class of methods is stable in the sense of zero-stability for arbitrary stepsize sequences. Furthermore there exist L(α)-stable methods with large α for s=4,...,8. Using the concept of effective order we derive methods having order s for constant stepsizes. Numerical experiments show an efficiency superior to RODAS for more stringent tolerances.