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

TL;DR

This paper introduces a meshless numerical method combining radial basis functions and Runge-Kutta integration to solve a family of generalized fifth-order Korteweg-de Vries equations with high accuracy.

Contribution

It presents a novel meshless approach using radial basis functions and Runge-Kutta methods for solving complex fifth-order KdV equations.

Findings

High accuracy demonstrated through comparison with exact solutions

Effective meshless method for complex nonlinear PDEs

Potential for application to other high-order equations

Abstract

In this paper we 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. This method exhibits high accuracy as seen from the comparison with the exact solutions.