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

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• 作者：J. Vigo-Aguiar^a ; ^b ; ^{jvigo@usal.es} ; Higinio Ramos^a ; ^c ; ^{higra@usal.es} ; C. Clavero^d ; ^{clavero@unizar.es}
• 关键词：65L05 ; 65L20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：599-603
• 全文大小：461 K
• 卷排序：318

文摘

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 term is of autonomous type affected by a perturbation parameter. The new 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 of problems, showing its good performance.