Twostep-by-twostep PIRK-type PC methods with continuous output formulas

DOI10.1016/j.cam.2007.10.003zbMath1156.65070OpenAlexW2049804259MaRDI QIDQ950087

Nguyen Huu Cong, Le Ngoc Xuan

Publication date: 22 October 2008

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.2007.10.003

zbMATH Keywords

stabilityinitial value problemRunge-Kutta methodscollocationpredictor-corrector methodsparallal computation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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 (5)

A variable step implicit block multistep method for solving first-order ODEs ⋮ 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 ⋮ Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs ⋮ Two-step-by-two-step PIRKN-type PC methods based on Gauss-Legendre collocation points for nonstiff IVPs

Cites Work

• Parallel methods for initial value problems
• Efficient block predictor-corrector methods with a small number of corrections
• Continuous variable stepsize explicit pseudo two-step RK methods
• Parallel block predictor-corrector methods of Runge-Kutta type
• Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems
• Parallel iterated methods based on multistep Runge-Kutta methods of Radau type
• An improvement for explicit parallel Runge-Kutta methods
• Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs
• Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer
• Parallel iteration of high-order Runge-Kutta methods with stepsize control
• A class of explicit parallel two-step Runge-Kutta methods
• Solving Ordinary Differential Equations I
• Block Runge-Kutta Methods on Parallel Computers
• High-order Explicit Runge-Kutta Formulae, Their Uses, and Limitations
• Parallel-Iterated RK-Type PC Methods With Continuous Output Formulas * This work was partly supported by N.R.P.F.S.
• Explicit pseudo two-step runge-kutta methods for parallel computers^∗
• Comparing Numerical Methods for Ordinary Differential Equations
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