Variable stepsize implementation of multistep methods for y''=f(x, y, y')

Authors:
Jesús Vigo-Aguiar;Higinio Ramos
Affiliations:
Facultad de Ciencias, Universidad de Salamanca, Salamanca, Spain;Escuela Politécnica Superior, Zamora, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Year:
2006

Citing 7
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Abstract

The Falkner method is a multistep scheme intended for the numerical solution of second-order initial value problems where the first derivative does appear explicitly. In this paper, we develop a procedure to obtain k-step Falkner methods (explicit and implicit) in their variable step-size versions, providing recurrence formulas to compute the coefficients efficiently. Considering a pair of explicit and implicit formulae, these may be implemented in predictor-corrector mode.