Preservation of equilibrium states and their stability for discrete Runge-Kutta approximations of continuous systems

DOI10.1007/BF02308829zbMath0873.65082OpenAlexW2057752569MaRDI QIDQ1360812

L. Z. Fishman

Publication date: 18 August 1997

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02308829

zbMATH Keywords

equilibrium pointsRunge-Kutta methodsecond-order systemEuler methodperiodic pointsstability region

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)

Cites Work

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• On the Numerical Approximation of Phase Portraits Near Stationary Points
• A Unified Approach to Spurious Solutions Introduced by Time Discretisation. Part I: Basic Theory
• THE DYNAMICS OF RUNGE–KUTTA METHODS