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

DOI10.1016/j.apnum.2005.04.024zbMath1089.65068OpenAlexW2004095437MaRDI QIDQ2489725

Bernhard A. Schmitt, Rüdiger Weiner, Helmut Podhaisky

Publication date: 28 April 2006

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2005.04.024

zbMATH Keywords

numerical resultsNordsieck representationGeneral linear methodsLinearly-implicit two-step methodsPeer-method

Mathematics Subject Classification ID

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

Related Items (12)

Convergence results of two-step W-methods for two-parameter singular perturbation problems ⋮ Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Functionally fitted explicit two step peer methods ⋮ On the derivation of explicit two-step peer methods ⋮ Explicit two-step peer methods ⋮ Peer methods for the one-dimensional shallow-water equations with CWENO space discretization ⋮ Generalized linear multistep methods for ordinary differential equations ⋮ A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems ⋮ Rosenbrock-type `peer' two-step methods ⋮ On quasi-consistent integration by Nordsieck methods ⋮ 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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• Construction of highly stable two-step W-methods for ordinary differential equations
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
• Two-step W-methods for stiff ODE systems
• Parallel `peer' two-step W-methods and their application to MOL-systems.
• Design, analysis and testing of some parallel two-step W-methods for stiff systems
• Unconditionally stable general linear methods for ordinary differential equations
• Rosenbrock-type `peer' two-step methods
• Implicit parallel peer methods for stiff initial value problems
• On error estimation in general linear methods for stiff ODEs
• Difference Methods for Stiff Ordinary Differential Equations
• Parallel Two-Step W-Methods with Peer Variables

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