Explicit pseudo two-step runge-kutta methods for parallel computers∗

DOI10.1080/00207169908804881zbMath0945.65081OpenAlexW2091032504MaRDI QIDQ4935391

Nguyen Huu Cong

Publication date: 5 October 2000

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207169908804881

zbMATH Keywords

stabilitynumerical experimentsparallel computationcollocationorder conditionscomparisonsexplicit pseudo two-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) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (13)

Collocation Runge–Kutta–Nyström methods for solving second-order initial value problems ⋮ Collocation-based two-step Runge-Kutta methods ⋮ Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs ⋮ Parallel-iterated pseudo two-step Runge-Kutta methods with step size control ⋮ Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points ⋮ A general class of explicit pseudo--two-step RKN methods on parallel computers ⋮ Explicit pseudo two-step exponential Runge-Kutta methods for the numerical integration of first-order differential equations ⋮ Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs ⋮ Twostep-by-twostep PIRK-type PC methods with continuous output formulas ⋮ Functionally fitted explicit pseudo two-step Runge-Kutta methods ⋮ Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer ⋮ Parallel-Iterated RK-Type PC Methods With Continuous Output Formulas * This work was partly supported by N.R.P.F.S. ⋮ Continuous variable stepsize explicit pseudo two-step RK methods

Cites Work

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• Collocation-based two-step Runge-Kutta methods
• A class of explicit parallel two-step Runge-Kutta methods
• Two-Step Runge–Kutta Methods
• High-order Explicit Runge-Kutta Formulae, Their Uses, and Limitations
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• Comparing Numerical Methods for Ordinary Differential Equations

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