B-convergence properties of defect correction methods. I, II

DOI10.1007/BF01389621zbMath0619.65061OpenAlexW2080617060MaRDI QIDQ1089752

B. George

Publication date: 1986

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133105

zbMATH Keywords

numerical experimentsorders of convergenceimplicit Euler schemeorder reductionglobal error boundsimplicit midpoint ruleB-convergencenonlinear stiff problemsRunge-Kutta-methodsiterated defect correction algorithms

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (5)

Higher-order additive Runge-Kutta schemes for ordinary differential equations ⋮ B-convergence: A survey ⋮ Stability and B-convergence of general linear methods ⋮ An error analysis of iterated defect correction methods for linear differential-algebraic equations ⋮ Asymptotic error expansions for stiff equations: Applications

Cites Work

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• B-convergence of the implicit midpoint rule and the trapezoidal rule
• Implementation of defect correction methods for stiff differential equations
• Discrete Newton methods and iterated defect corrections
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• A stability property of implicit Runge-Kutta methods
• On the implementation of implicit Runge-Kutta methods
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
• OnA-stable implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods

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