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Variable stepsize Störmer-Cowell methods. (English) Zbl 1092.65060
Authors’ summary: Störmer and Cowell methods are multistep codes for the numerical solution of second-order initial value problems where the first derivative does not appear explicitly. In this paper, we develop a procedure to obtain \(k\)-step Störmer and Cowell methods in their variable step size version, avoiding computation of the coefficients by recurrences or integrals. We offer a strategy for conveniently selecting the stepsize. Considering a pair of explicit and implicit formulae, these may be implemented in a predictor-corrector mode.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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