RBF-FD Method for Some Dispersive Wave Equations and Their Eventual Periodicity

TL;DR

This paper introduces a radial basis function finite difference method combined with RK4 for solving dispersive wave equations, effectively capturing solutions and their eventual periodicity on bounded domains.

Contribution

It presents a novel local numerical scheme using radial kernels and RK4 for dispersive wave equations, demonstrating efficiency and validation against existing methods.

Findings

Accurately approximates solutions of dispersive wave equations.

Effectively captures eventual periodicity of solutions.

Demonstrates computational efficiency due to sparse matrices.

Abstract

In this paper, we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of (IBVPs) for some dispersive wave equations on a bounded domain corresponding to periodic forcing. The constructed numerical scheme is based on radial kernels and local in nature like finite difference method. The temporal variable is executed through RK4 scheme. Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution. The results achieved are validated and examined with other methods accessible in the literature.