Extrapolation at stiff differential equations

DOI10.1007/BF01462235zbMath0643.65034MaRDI QIDQ1102075

Ernst Hairer, Christian Lubich

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/133242

zbMATH Keywords

error estimationimplicit Euler methodextrapolation methodsglobal errorimplicit midpoint rulestep-size controlNumerical examplesstiff initial value problemsAsymptotic expansions

Mathematics Subject Classification ID

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

Related Items (11)

Time-accurate and highly-stable explicit operators for stiff differential equations ⋮ A note on convergence concepts for stiff problems ⋮ Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations ⋮ Linearly implicit extrapolation methods for differential-algebraic systems ⋮ Dense output for extrapolation methods ⋮ Modern convergence theory for stiff initial-value problems ⋮ Vienna contributions to the development of RK-methods ⋮ On the error structure of the implicit Euler scheme applied to stiff systems of differential equations ⋮ Asymptotic error expansions for stiff equations: Applications ⋮ On error structures and extrapolation for stiff systems, with application in the method of lines ⋮ Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case

Uses Software

• DEPAC

Cites Work

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• Order and stepsize control in extrapolation methods
• A semi-implicit mid-point rule for stiff systems of ordinary differential equations
• Asymptotic expansions of the global error of fixed-stepsize methods
• One-step and extrapolation methods for differential-algebraic systems
• Numerical treatment of ordinary differential equations by extrapolation methods
• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• D-Stability
• An Analysis of Rosenbrock Methods for Nonlinear Stiff Initial Value Problems
• Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme
• On Extrapolation Algorithms for Ordinary Initial Value Problems

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