A first approach in solving initial-value problems in ODEs by elliptic fitting methods

摘要

Exponentially-fitted and trigonometrically-fitted methods have a long successful history in the solution of initial-value problems, but other functions might be considered in adapted methods. Specifically, this paper aims at the derivation of a new numerical scheme for approximating initial Value problems of ordinary differential equations using elliptic functions. The example considered is the undamped Duffing equation where the forcing MSC: term is of autonomous type affected by a perturbation parameter. The hew scheme is constructed by considering a suitable approximation to the theoretical solution based on elliptic functions. The proposed elliptic fitting procedure has been tested on a variety problems, showing its good performance. (C) 2015 Elsevier B.V. All rights reserved.