Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations

DOI10.1016/j.apnum.2004.08.010zbMath1086.65069OpenAlexW2068711724MaRDI QIDQ1772791

Zdzisław Jackiewicz, Zbigniew Bartoszewski

Publication date: 21 April 2005

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.010

zbMATH Keywords

numerical exampleserror estimationNordsieck representationtwo-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)

Related Items (15)

Two-step almost collocation methods for ordinary differential equations ⋮ Order conditions for integrators and mappings with applications ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ Derivation of continuous explicit two-step Runge-Kutta methods of order three ⋮ Two-step Runge-Kutta methods with quadratic stability functions ⋮ Explicit Nordsieck methods with quadratic stability ⋮ Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection ⋮ 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 ⋮ Continuous two-step Runge-Kutta methods for ordinary differential equations ⋮ Construction and implementation of highly stable two-step continuous methods for stiff differential systems ⋮ Improved Euler-Maruyama method for numerical solution of the Itô stochastic differential systems by composite previous-current-step idea ⋮ Two-step almost collocation methods for Volterra integral equations ⋮ EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS

Uses Software

• Matlab
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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