Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations

DOI10.1007/BF02142812zbMath0869.65050OpenAlexW1994213792MaRDI QIDQ1815706

S. Tracogna, Zdzisław Jackiewicz

Publication date: 11 August 1997

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02142812

zbMATH Keywords

stabilityconvergencenumerical examplesvariable stepsizezero-stabilityRunge-Kutta formulasone stage algorithms

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

• Numerical treatment of O.D.Es.: The theory of A-methods
• Diagonally-implicit multi-stage integration methods
• Elements of a general theory of composite integration methods
• Explicit two-step Runge-Kutta methods
• Variable-Stepsize Explicit Two-Step Runge-Kutta Methods
• The Effect of Variable Mesh Size on the Stability of Multistep Methods
• A New Theoretical Approach to Runge–Kutta Methods
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Comparing Numerical Methods for Ordinary Differential Equations
• Implementation of two-step Runge-Kutta methods for ordinary differential equations