On the existence of solution of stage equations in implicit Runge-Kutta methods

DOI10.1016/S0377-0427(99)00129-6zbMath0942.65076MaRDI QIDQ1964099

S. González-Pinto, Manuel Calvo, Juan I. Montijano

Publication date: 3 February 2000

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

zbMATH Keywords

implicit Runge-Kutta methodsdissipative problemsBSI-stabilitystage equations

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 (1)

A general class of linear unconditionally energy stable schemes for the gradient flows

Cites Work

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• On the unique solvability of the Runge-Kutta equations
• On the solvability of the systems of equations arising in implicit Runge- Kutta methods
• Contractivity of Runge-Kutta methods
• Contractivity in the numerical solution of initial value problems
• On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods
• On the Algebraic Equations in Implicit Runge–Kutta Methods
• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems

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