An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations. Issue 6 (3rd July 2018)

• Record Type: Journal Article
• Authors: Durán, A.
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 6/7(2018)
• Page Start: 1362
• Page End: 1374
• Publication Date: 2018-07-03
• Subjects: Fractional KdV equations -- solitary waves -- Petviashvili method -- acceleration techniques; 65H10 -- 65M70 -- 65Z05; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1422732
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg–de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation techniques of acceleration. This combination improves the performance in both the velocity of convergence and the computation of profiles for limiting values of the fractional parameter. The algorithm is described and numerical experiments of validation are presented. The accuracy attained by the procedure can be used to investigate additional properties of the waves. This approach is illustrated here by analysing the speed–amplitude relation.