A method for constructing generalized Runge-Kutta methods

DOI10.1016/0377-0427(91)90185-MzbMath0747.65062MaRDI QIDQ1184137

Tatsuo Torii, Sugiura, Hiroshi

Publication date: 28 June 1992

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityCauchy problemerror estimationaccuracynumerical testslinear equationsgeneralized Runge-Kutta methodsNewton iteration processimplicit Runge-Kutta formula

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) 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)

Related Items

The use of Butcher series in the analysis of Newton-like iterations in Runge-Kutta formulas, New charge simulation method for numerical conformal mapping of ring domains

Uses Software

• ODEPACK

Cites Work

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• The numerical solution of differential-algebraic systems by Runge-Kutta methods
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• The Concept of B-Convergence
• Comparing numerical methods for stiff systems of O.D.E:s
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• On the implementation of implicit Runge-Kutta methods
• An Efficient Solution Process for Implicit Runge–Kutta Methods
• Stability Criteria for Implicit Runge–Kutta Methods
• A stopping criterion for the Newton-Raphson method in implicit multistep integration algorithms for nonlinear systems of ordinary differential equations
• The implementation of Runge-Kutta implicit processes
• Implicit Runge-Kutta Processes