Parallel block predictor-corrector methods of Runge-Kutta type

DOI10.1016/0168-9274(93)90135-EzbMath0786.65060MaRDI QIDQ1308565

P. J. van der Houwen, Nguyen Huu Cong

Publication date: 6 January 1994

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

zbMATH Keywords

stabilityparallel computingRunge-Kutta methodstest problemscost reductionblock predictor-corrector methodsblock parallel implicit RK methodsRunge-Kutta correctors

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

Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems, Preconditioning in implicit initial-value problem methods on parallel computers, Explicit symmetric Runge-Kutta-Nyström methods for parallel computers, 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, On a parallel mesh-chopping algorithm for a class of initial value problems using fourth-order explicit Runge-Kutta method, Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points, Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs, Twostep-by-twostep PIRK-type PC methods with continuous output formulas, A class of explicit parallel two-step Runge-Kutta methods, Explicit pseudo two-step runge-kutta methods for parallel computers^∗, 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., Explicit parallel two-step Runge-Kutta-Nyström methods, Parallel block pc methods with rkn-type correctors and adams-type predictors^∗, Continuous variable stepsize explicit pseudo two-step RK methods, Explicit, high-order Runge-Kutta-Nyström methods for parallel computers, RKN-type parallel block PC methods with Lagrange-type predictors

Cites Work

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• The search for the Holy Grail, or: Predictor-corrector methods for solving ODEIVPs
• Efficient block predictor-corrector methods with a small number of corrections
• The error behaviour of a general class of predictor-corrector methods
• Parallel defect control
• Parallel iteration of high-order Runge-Kutta methods with stepsize control
• Parallel Solution of ODE’<scp>s</scp> by Multiblock Methods
• Block Runge-Kutta Methods on Parallel Computers
• Parallel Methods for the Numerical Solution of Ordinary Differential Equations
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• Parallel Methods for the Numerical Integration of Ordinary Differential Equations
• Block Implicit One-Step Methods
• Cyclic Composite Multistep Predictor-Corrector Methods