A meshless numerical solution of the family of generalized fifth‐order Korteweg‐de Vries equations

Abstract

Purpose

The purpose of this paper is to present a numerical solution of a family of generalized fifth‐order Korteweg‐de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge‐Kutta method as a time integrator and exhibits high accuracy as seen from the comparison with the exact solutions.

Design/methodology/approach

The study uses a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge‐Kutta method as a time integrator.

Findings

The paper reveals that this method exhibits high accuracy as seen from the comparison with the exact solutions.

Originality/value

This method is efficient method as it is easy to implement for the numerical solutions of PDEs.

Citation

Tauseef Mohyud‐Din, S., Negahdary, E. and Usman, M. (2012), "A meshless numerical solution of the family of generalized fifth‐order Korteweg‐de Vries equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 5, pp. 641-658. https://doi.org/10.1108/09615531211231280