Adaptive moving mesh for solving the korteweg-de vries-burgers equation

Abstract

This paper presents an adaptive mesh method for solving the Kortewegde Vries-Burgers (KdVB) equation numerically. The r-adaptive mesh method which employs a monitor function and one of the mesh equations (MMPDEs) presented by [11] which uses to concentrate and move the mesh. This technique correctly resolves the various structures seen in these problems. Furthermore, it decreases the computational effort in comparison to the numerical solution using a fixed uniform mesh scheme. Here, the exact solution of the KdVB equation at a fixed time is utilized to compare with that employing an adaptive moving mesh and a uniform mesh. By comparing the relative error for the obtained solutions of the problem, I will check the accuracy of the adaptive method.