A note on convergence concepts for stiff problems

DOI10.1007/BF02262216zbMath0719.65058MaRDI QIDQ2640324

Winfried Auzinger, Reinhard Frank, Gabriela Kirlinger

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical examplessingular perturbationsstiff differential equationsstiff problemslogarithmic normsone- sided Lipschitz continuity

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) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13)

Related Items (12)

A NOTE ON LYAPUNOV TRANSFORMATION AND EXPONENTIAL DECAY IN LINEAR ODE SYSTEMS ⋮ A NORMAL FORM FOR MULTISTEP COMPANION MATRICES ⋮ Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities ⋮ Two methods for the implicit integration of stiff reaction systems ⋮ An extension of B-convergence for Runge-Kutta methods ⋮ Modern convergence theory for stiff initial-value problems ⋮ Extending convergence of BDF methods for a class of nonlinear strongly stiff problems ⋮ Linear multistep methods applied to stiff initial value problems -- a survey ⋮ The analytic and numerical stability of stiff impulsive differential equations in Banach space ⋮ Vienna contributions to the development of RK-methods ⋮ Extending convergence theory for nonlinear stiff problems. I ⋮ Stability and $B$-convergence properties of multistep Runge-Kutta methods

Cites Work

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• Extrapolation at stiff differential equations
• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Asymptotic error expansions for stiff equations: Applications
• Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• D-Stability
• A stability property of implicit Runge-Kutta methods
• Difference Methods for Stiff Ordinary Differential Equations

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