Predictor-corrector methods with improved absolute stability regions. (English) Zbl 0533.65045

For the initial value problem of a first order differential equation \(dy/dt=f(t,y)\) a family of predictor-corrector type methods of order \(p>2\) and enlarged stability interval is constructed. The stability analysis for the equation are given. A computational scheme is constructed using Chebyshev recursion. The results are applied to the case where the predictor formula is defined by extrapolation and the corrector formula by backward differentiation obtaining methods of order up to \(p=6\). An extension to the equation \(d^ ny/dt^ n=f(t,y)\) and an application to second-order differential equations appeared in Math. Cent., Amst. Afd. Numer. Wiskd. NW 137/82 (1982).
Reviewer: A.de Castro


65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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