Stability of Runge-Kutta-Nyström methods

DOI10.1016/j.cam.2005.01.005zbMath1089.65076OpenAlexW2039285284MaRDI QIDQ818162

M. J. Moreta, Begoña Cano, Isaías Alonso-Mallo

Publication date: 24 March 2006

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.01.005

zbMATH Keywords

stabilitycomparison of methodsnumerical examplesRunge-Kutta-Nyström methodsstiff problems

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)

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Cites Work

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• Numerical range and functional calculus in Hilbert space
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• A P-stable singly diagonally implicit Runge-Kutta-Nyström method
• Analysis of error growth via stability regions in numerical initial value problems
• Order reduction and how to avoid it when explicit Runge-Kutta-Nyström methods are used to solve linear partial differential equations
• Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
• From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy Method
• Four-stage symplectic and P-stable SDIRKN methods with dispersion of high order