Implicit parallel peer methods for stiff initial value problems

DOI10.1016/j.apnum.2004.08.019zbMath1072.65108OpenAlexW1979279579MaRDI QIDQ1772812

Karin Erdmann, Rüdiger Weiner, Bernhard A. Schmitt

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.019

zbMATH Keywords

stabilitynumerical examplesparallel computationstiff systemssingularly perturbationPeer methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) 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) Singular perturbations for ordinary differential equations (34E15)

Related Items (28)

IMEX peer methods for fast-wave-slow-wave problems ⋮ Exponential Krylov peer integrators ⋮ Superconvergent explicit two-step peer methods ⋮ Convergence results of two-step W-methods for two-parameter singular perturbation problems ⋮ Discrete adjoint implicit peer methods in optimal control ⋮ Two-step peer methods with continuous output ⋮ A class of implicit peer methods for stiff systems ⋮ Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods ⋮ Functionally fitted explicit two step peer methods ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ On the implementation of explicit two-step peer methods with Runge-Kutta stability ⋮ On the derivation of explicit two-step peer methods ⋮ Extrapolation-based implicit-explicit Peer methods with optimised stability regions ⋮ Extrapolation-based super-convergent implicit-explicit peer methods with A-stable implicit part ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ Explicit two-step peer methods ⋮ Exponential peer methods ⋮ On algebraic stability of general linear methods and peer methods ⋮ 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 ⋮ Superconvergent IMEX peer methods ⋮ Stability and consistency of discrete adjoint implicit peer methods ⋮ Linearly-implicit two-step methods and their implementation in Nordsieck form ⋮ Rosenbrock-type `peer' two-step methods ⋮ Implicit peer methods for large stiff ODE systems ⋮ Parameter optimization for explicit parallel peer two-step methods ⋮ Adapted explicit two-step peer methods ⋮ Multi-implicit peer two-step W-methods for parallel time integration

Uses Software

• RODAS

Cites Work

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• On the convergence of multistep methods for nonlinear stiff differential equations
• General linear method: A survey
• Convergence results for general linear methods on singular perturbation problems
• Parallel `peer' two-step W-methods and their application to MOL-systems.
• Multi-implicit peer two-step W-methods for parallel time integration
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Parallel Two-Step W-Methods with Peer Variables

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