Implementation of two-step Runge-Kutta methods for ordinary differential equations

DOI10.1016/S0377-0427(96)00093-3zbMath0871.65072MaRDI QIDQ5961650

S. Tracogna

Publication date: 9 October 1997

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

zbMATH Keywords

numerical experimentsmultistep methodsstepsize controllocal error estimationcontinuous interpolantNordsieck techniquestwo-step Runge-Kutta methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Order reduction phenomenon for general linear methods, Two-step almost collocation methods for ordinary differential equations, Two-step Runge-Kutta methods with quadratic stability functions, Second derivative two-step collocation methods for ordinary differential equations, Construction of two-step Runge--Kutta methods with large regions of absolute stability, Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection, Efficient two-step Runge-Kutta methods for fluid dynamics simulations, Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations, Order conditions for general linear methods, Search for efficient general linear methods for ordinary differential equations, Derivation and implementation of two-step Runge-Kutta pairs, Continuous two-step Runge-Kutta methods for ordinary differential equations, Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations, Two-step almost collocation methods for Volterra integral equations, Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations, Construction of two-step Runge-Kutta methods of high order of ordinary differential equations, A class of two-derivative two-step Runge-Kutta methods for non-stiff ODEs, EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS, Stability analysis of two-step Runge-Kutta methods for delay differential equations

Cites Work

• Unnamed Item
• Numerical treatment of O.D.Es.: The theory of A-methods
• Diagonally-implicit multi-stage integration methods
• Diagonally implicit general linear methods for ordinary differential equations
• Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
• Explicit two-step Runge-Kutta methods
• Two-Step Runge-Kutta Methods and Hyperbolic Partial Differential Equations
• On Numerical Integration of Ordinary Differential Equations
• Two-Step Runge–Kutta Methods
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• A Class of Variable-Step Explicit Nordsieck Multivalue Methods
• Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations
• Pseudo-Runge-Kutta Methods Involving Two Points
• Generalized Multistep Predictor-Corrector Methods
• Hybrid Methods for Initial Value Problems in Ordinary Differential Equations
• Cyclic Composite Multistep Predictor-Corrector Methods