Convergence of linear multistep methods for two-parameter singular perturbation problems

DOI10.1007/BF02669574zbMath0990.65089MaRDI QIDQ5942764

Hongyuan Fu, Shou-fu Li, Ai-Guo Xiao, Guangnan Chen

Publication date: 19 March 2002

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergencesystemssingular perturbationnumerical exampleserror boundslinear multistep methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

Convergence results of two-step W-methods for two-parameter singular perturbation problems ⋮ Convergence of parallel multistep hybrid methods for singular perturbation problems

Uses Software

• RODAS

Cites Work

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• Stability and B-convergence of general linear methods
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• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
• Order results for Rosenbrock type methods on classes of stiff equations
• Convergence results for general linear methods on singular perturbation problems
• Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type. I: RK- methods
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• B-Convergence Properties of Multistep Runge-Kutta Methods
• Runge–Kutta Solutions of Stiff Differential Equations Near Stationary Points

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