Petviashvili type methods for traveling wave computations: I. Analysis of convergence

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• 作者：J. Á ; lvarez^a ; ^b ; ^{joralv@eii.uva.es" class="auth_mail} ; A. Durá ; n^c ; ^b ; ^{angel@mac.uva.es" class="auth_mail}
• 关键词：65H10 ; 65M99 ; 35C99 ; 35C07 ; 76B25
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：15 August, 2014
• 年：2014
• 卷：266
• 期：Complete
• 页码：39-51
• 全文大小：689 K

文摘

In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out.