Efficient block predictor-corrector methods with a small number of corrections

DOI10.1016/0377-0427(93)90270-LzbMath0782.65088MaRDI QIDQ688031

Kevin Burrage

Publication date: 28 February 1994

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

zbMATH Keywords

numerical examplecollocation methoderror analysisparallelism\(B\)-seriesblock predictor-corrector methodsnonstiff ordinary differential equations

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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

A variable step implicit block multistep method for solving first-order ODEs, Preconditioning in implicit initial-value problem methods on parallel computers, Block predictor-corrector schemes for the parallel solution of ODEs, Parallel iteration across the steps of high-order Runge-Kutta methods for nonstiff initial value problems, 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, Parallel iteration schemes for implicit ODEIVP methods, Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points, Closed-form solutions to differential equations via differential evolution, A large parallel block predictor-corrector method for initial value problems, Improved parallel-iterated pseudo two-step RK methods for nonstiff IVPs, Twostep-by-twostep PIRK-type PC methods with continuous output formulas, Parallel methods for initial value problems, Derivation of new block methods for the numerical solution of first-order IVP's, Explicit pseudo two-step runge-kutta methods for parallel computers^∗, CWI contributions to the development of parallel 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., An analysis of the order of Runge-Kutta methods that use an iterative scheme to compute their internal stage values, Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs, Continuous variable stepsize explicit pseudo two-step RK methods, Parallel block predictor-corrector methods of Runge-Kutta type

Cites Work

• High order embedded Runge-Kutta formulae
• The error behaviour of a general class of predictor-corrector methods
• On the Butcher group and general multi-value methods
• Iterated Runge–Kutta Methods on Parallel Computers
• Order Properties of Implicit Multivalue Methods for Ordinary Differential Equations
• Block Runge-Kutta Methods on Parallel Computers
• Waveform Iteration and the Shifted Picard Splitting
• The Potential for Parallelism in Runge–Kutta Methods. Part 1: RK Formulas in Standard Form
• A Runge-Kutta for all Seasons
• Unnamed Item