Starting methods for two-step Runge-Kutta methods of stage-order 3 and order 6

DOI10.1016/j.cam.2005.03.012zbMath1079.65078OpenAlexW2044707580MaRDI QIDQ2570084

James H. Verner

Publication date: 26 October 2005

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.2005.03.012

zbMATH Keywords

numerical examplesImplementationOrder reductionOrder conditionsTwo-step Runge-Kutta methodsStarting 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 (5)

Bifurcation \& chaos in nonlinear structural dynamics: novel \& highly efficient optimal-feedback accelerated Picard iteration algorithms ⋮ Subquadrature expansions for TSRK methods ⋮ Improved starting methods for two-step Runge-Kutta methods of stage-order \(p\)-3 ⋮ Starting procedures for general linear methods ⋮ A unified starting procedure for the Houbolt method

Cites Work

• Derivation and implementation of two-step Runge-Kutta pairs
• High order embedded Runge-Kutta formulae
• Two-step Runge-Kutta: Theory and practice
• Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error
• Completely Imbedded Runge–Kutta Pairs
• Order Conditions for General Two-Step Runge--Kutta Methods
• A New Theoretical Approach to Runge–Kutta Methods
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Comparing Numerical Methods for Ordinary Differential Equations

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