Petviashvili type methods for traveling wave computations: II. Acceleration with vector extrapolation methods

J. Álvarez and A. Durán

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 123, issue C, 19-36

Abstract: In this paper a family of fixed point algorithms, generalizing the Petviashvili method, is considered. A previous work studied the convergence of the methods. Presented here is a second part of the analysis, concerning the introduction of acceleration techniques, based on vector extrapolation, into the iterative procedures. The purpose of the research is two-fold: one is improving the performance of the methods in case of convergence and the second one is widening their application when generating traveling waves in nonlinear dispersive wave equations, transforming some divergent into convergent cases. A comparative study through several numerical experiments is carried out.

Keywords: Petviashvili type methods; Traveling wave generation; Iterative methods for nonlinear systems; Acceleration techniques; Vector extrapolation methods (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:123:y:2016:i:c:p:19-36

DOI: 10.1016/j.matcom.2015.10.015

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