Design, analysis and testing of some parallel two-step W-methods for stiff systems

DOI10.1016/S0168-9274(01)00162-3zbMath1005.65073OpenAlexW1991214860MaRDI QIDQ1612469

Bernhard A. Schmitt, Helmut Podhaisky, Rüdiger Weiner

Publication date: 22 August 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00162-3

zbMATH Keywords

stabilityconvergencenumerical examplesparallel computationstiff systemsKrylov techniquestwo-step W-methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Convergence results of two-step W-methods for two-parameter singular perturbation problems, Two-step almost collocation methods for ordinary differential equations, Construction of highly stable two-step W-methods for ordinary differential equations, On the implementation of explicit two-step peer methods with Runge-Kutta stability, Parallel `peer' two-step W-methods and their application to MOL-systems., A comparison of one-step and two-step W-methods and peer methods with approximate matrix factorization, Linearly implicit GARK schemes, Linearly-implicit two-step methods and their implementation in Nordsieck form, Rosenbrock-type `peer' two-step methods, Parallel two-step ROW-methods for stiff delay differential equations, Rational homotopy perturbation method for solving stiff systems of ordinary differential equations, Rosenbrock-Wanner Methods: Construction and Mission, Two-Step W-Methods, A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• RADAU
• ROWMAP

Cites Work

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• Order and stability of parallel methods for stiff problems
• Parallel linear system solvers for Runge-Kutta methods
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• The choice of parameters in parallel general linear methods for stiff problems
• Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer
• Stiff differential equations solved by Radau methods
• Exponential Integrators for Large Systems of Differential Equations