Embedded Runge-Kutta formulae with stable equilibrium states

DOI10.1016/0377-0427(90)90192-3zbMath0704.65054OpenAlexW2024534901MaRDI QIDQ917230

Elsie Sterbin Gottlieb

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90192-3

zbMATH Keywords

step size controlRunge-Kutta pairsregion of absolute stabilityembedded Runge-Kutta formulaestable equilibrium states

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)

Related Items (5)

A new stepsize strategy for explicit Runge-Kutta codes ⋮ A PI stepsize control for the numerical solution of ordinary differential equations ⋮ Control of local error stabilizes integrations ⋮ Time-step selection algorithms: adaptivity, control, and signal processing ⋮ Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics

Cites Work

• Unnamed Item
• A reconsideration of some embedded Runge-Kutta formulae
• A family of embedded Runge-Kutta formulae
• High order embedded Runge-Kutta formulae
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• Equilibrium states of Runge Kutta schemes
• Equilibrium states of Runge-Kutta schemes: part II
• Analysis of Stepsize Selection Schemes for Runge-Kutta Codes
• On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations

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