A Meshless method of lines for the numerical solution of Coupled Drinfeld's-Sokolov-Wilson System

TL;DR

This paper introduces a meshless method of lines using radial basis functions combined with Runge-Kutta time integration to solve the Coupled Drinfeld's-Sokolov-Wilson System, demonstrating improved accuracy over existing methods.

Contribution

It presents a novel meshless approach with RBFs and Runge-Kutta for this complex system, enhancing solution accuracy and computational efficiency.

Findings

Achieved higher accuracy (L2 and L1) compared to previous methods.

Validated the method's effectiveness through numerical experiments.

Demonstrated the method's potential for solving similar coupled systems.

Abstract

This paper applies meshless method of lines, which uses radial basis functions (RBFs) as a spatial collocation scheme to solve the Coupled Drinfeld's-Sokolov-Wilson System. Runge-Kutta method is used for time integration of the system of ODEs obtained as a result of spatial discretization in contrast to usual RBFs or finite difference methods. Accuracy (L2 and L1) is compared with the existing results from other methods available in the literature.