Order conditions for integrators and mappings with applications

DOI10.1016/j.na.2006.09.025zbMath1128.65059OpenAlexW2080505432MaRDI QIDQ2643453

Xin-Yuan Wu

Publication date: 23 August 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.09.025

zbMATH Keywords

linear multistep methodsorder conditionstwo-step Runge-Kutta methodssecond-derivative linear multistep methodsRunge-Kutta-like methodorder conditions based on mappingsthree-step Runge-Kutta methods

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 new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators

Cites Work

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• Numerical treatment of O.D.Es.: The theory of A-methods
• On the Butcher group and general multi-value methods
• Order conditions for two-step Runge-Kutta methods
• A class of Runge-Kutta formulae of order three and four with reduced evaluations of function
• Runge-Kutta with higher order derivative approximations
• Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
• Two-step Runge-Kutta methods of order over five with reduced function evaluations
• Order Conditions for General Two-Step Runge--Kutta Methods
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• An Algebraic Theory of Integration Methods

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