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.
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