Multistride \(L\)-stable fourth-order methods for the numerical solution of ODEs

DOI10.1016/0898-1221(96)00149-6zbMath0866.65052OpenAlexW2017136807MaRDI QIDQ1352747

T. Van Hecke, H. E. De Meyer, Guido Vanden Berghe, Marnix van Daele

Publication date: 8 April 1997

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(96)00149-6

zbMATH Keywords

\(A\)-stabilitylinear multistep methodsSimpson's rule\(L\)-stabilitymono-implicit Runge-Kutta methodsdouble-stride \(L\)-stable methods

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (2)

On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods ⋮ Optimal extended one-step schemes of exponential type for stiff initial-value problems

Cites Work

• An \(A\)-stable extended trapezoidal rule for the integration of ordinary differential equations
• A class of stabilized extended one-step methods for the numerical solution of ODEs
• Extended double-stride \(L\)-stable methods for the numerical solution of ODEs
• A general theory of stabilized extended one-step methods for odes
• Extended one-step methods for the numerical solution of ordinary differential equations
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• Order Results for Mono-Implicit Runge–Kutta Methods
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