An extension of B-convergence for Runge-Kutta methods

DOI10.1016/0168-9274(92)90008-2zbMath0747.65056OpenAlexW2049344980MaRDI QIDQ1184012

Gabriela Kirlinger, Winfried Auzinger, Reinhard Frank

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1016/0168-9274(92)90008-2

zbMATH Keywords

implicit Runge-Kutta methods\(B\)-stabilityglobal error boundsone-step methodsstiff initial value problems\(B\)-convergencenon-autonomous weakly nonlinear stiff systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Multiple scale methods for ordinary differential equations (34E13)

Related Items (5)

On a Newton-type method for differential-algebraic equations ⋮ A variable step-size implementation of a variational method for stiff differential equations ⋮ Modern convergence theory for stiff initial-value problems ⋮ Vienna contributions to the development of RK-methods ⋮ Stability and $B$-convergence properties of multistep Runge-Kutta methods

Cites Work

• Unnamed Item
• Unnamed Item
• Error bounds for the solution to the algebraic equations in Runge-Kutta methods
• On the convergence of multistep methods for nonlinear stiff differential equations
• On the unique solvability of the Runge-Kutta equations
• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Sur la B-stabilité des méthodes de Runge-Kutta
• Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
• A note on convergence concepts for stiff problems
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Asymptotic Expansions of the Global Discretization Error for Stiff Problems
• The Concept of B-Convergence
• D-Stability
• A stability property of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods
• Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme

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