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Efficient block predictor-corrector methods with a small number of corrections. (English) Zbl 0782.65088

For the numerical solution of nonstiff ordinary differential equations in a parallel environment block predictor-corrector methods are considered. A numerical example illustrates that the application of low-order predictors is not very efficient. Consequently, the use of high-order predictors together with a few correction steps is proposed. Based on a detailed error analysis of such methods (using \(B\)-series) a new corrector (collocation method) is derived.
Reviewer: E.Hairer (Genève)

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65Y05 Parallel numerical computation
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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