An efficient method to compute solitary wave solutions of fractional Korteweg-de Vries equations. (English) Zbl 1499.65185
Summary: 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.
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65Z05 | Applications to the sciences |
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