Parallel `peer' two-step W-methods and their application to MOL-systems.

DOI10.1016/j.apnum.2003.10.005zbMath1042.65072OpenAlexW2084548243MaRDI QIDQ1426336

Rüdiger Weiner, Bernhard A. Schmitt, Helmut Podhaisky

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2003.10.005

zbMATH Keywords

stabilityconvergencenumerical examplesparallel computationmethod of linesstiff ODEsnumerical comparisonMOLparallel two-step W methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (18)

Superconvergent explicit two-step peer methods ⋮ Convergence results of two-step W-methods for two-parameter singular perturbation problems ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Explicit two-step peer methods ⋮ Linearly implicit peer methods for the compressible Euler equations ⋮ Peer methods for the one-dimensional shallow-water equations with CWENO space discretization ⋮ Global error estimation and control in linearly-implicit parallel two-step peer W-methods ⋮ Linearly implicit GARK schemes ⋮ On the construction of restricted-denominator exponential W-methods ⋮ Linearly-implicit two-step methods and their implementation in Nordsieck form ⋮ Partially implicit peer methods for the compressible Euler equations ⋮ Rosenbrock-type `peer' two-step methods ⋮ Implicit parallel peer methods for stiff initial value problems ⋮ High-order linearly implicit two-step peer - finite element methods for time-dependent PDEs ⋮ Multi-implicit peer two-step W-methods for parallel time integration ⋮ A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

Uses Software

• ROWMAP

Cites Work

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• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• Two-step W-methods for stiff ODE systems
• Design, analysis and testing of some parallel two-step W-methods for stiff systems
• Solving Ordinary Differential Equations I
• Exponential Integrators for Large Systems of Differential Equations
• Parallel Two-Step W-Methods with Peer Variables
• Matrix-Free Methods for Stiff Systems of ODE’s

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