An introduction to ``Almost Runge-Kutta methods

DOI10.1016/S0168-9274(97)00030-5zbMath0905.65085OpenAlexW1989572481MaRDI QIDQ1360554

John C. Butcher

Publication date: 3 January 1999

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(97)00030-5

zbMATH Keywords

stabilitynumerical exampleserror estimationRunge-Kutta methodsstepsize controlstage ordermultivalue methodscontinuous output

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) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Pseudo-Runge-Kutta Methods Involving Two Points
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages