Analysis of a multirate theta-method for stiff ODEs

DOI10.1016/j.apnum.2008.03.022zbMath1163.65049OpenAlexW2153562486MaRDI QIDQ1007391

Willem H. Hundsdorfer, Valeriu Savcenco

Publication date: 20 March 2009

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

Full work available at URL: https://research.tue.nl/nl/publications/analysis-of-a-multirate-thetamethod-for-stiff-odes(64a2a49d-ffaf-4396-a0d1-f2f811b8b418).html

zbMATH Keywords

stabilitynumerical experimentserror estimationStiff differential systemsAnalysis of multirate time steppingautomatic step size partitioningTheta method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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A linearly fourth order multirate Runge-Kutta method with error control ⋮ A hybrid implicit-explicit adaptive multirate numerical scheme for time-dependent equations ⋮ Extrapolated multirate methods for differential equations with multiple time scales ⋮ A self adjusting multirate algorithm for robust time discretization of partial differential equations ⋮ Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1 ⋮ Comparison of the asymptotic stability properties for two multirate strategies ⋮ Multirate Numerical Integration for Stiff ODEs ⋮ Implicit multirate GARK methods ⋮ Comparison of the asymptotic stability for multirate Rosenbrock methods ⋮ A posteriori analysis of a multirate numerical method for ordinary differential equations ⋮ Fractional-step \(\theta\)-method for solving singularly perturbed problem in ecology ⋮ Construction of a multirate RODAS method for stiff ODEs ⋮ Efficient simulation of a slow-fast dynamical system using multirate finite difference schemes

Uses Software

• RODAS

Cites Work

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