Derivation and implementation of two-step Runge-Kutta pairs

DOI10.1007/BF03167454zbMath1006.65075OpenAlexW2041934546MaRDI QIDQ698393

Zdzisław Jackiewicz, James H. Verner

Publication date: 16 February 2003

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

Full work available at URL: https://doi.org/10.1007/bf03167454

zbMATH Keywords

error boundsRunge-Kutta methodsrobust step size controltwo-step pairs

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 (21)

Two-step almost collocation methods for ordinary differential equations ⋮ Numerically optimal Runge-Kutta pairs with interpolants ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ Estimating the error in the classical Runge-Kutta methods ⋮ Two-step Runge-Kutta methods with quadratic stability functions ⋮ Explicit Nordsieck methods with quadratic stability ⋮ Construction of two-step Runge--Kutta methods with large regions of absolute stability ⋮ Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection ⋮ Search for highly stable two-step Runge-Kutta methods ⋮ On explicit two-derivative two-step Runge-Kutta methods ⋮ Subquadrature expansions for TSRK methods ⋮ 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 ⋮ Improved starting methods for two-step Runge-Kutta methods of stage-order \(p\)-3 ⋮ 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 ⋮ Starting methods for two-step Runge-Kutta methods of stage-order 3 and order 6 ⋮ A class of two-derivative two-step Runge-Kutta methods for non-stiff ODEs ⋮ EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS

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