Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2020 / Cilt: 10 - Sayı: 4

ADAPTIVE MOVING MESH FOR SOLVING THE KORTEWEG-DEVRIES-BURGERS EQUATION

Abdulghani ALHARBI

Sayfa
897–908
DOI
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Özet

Abstract.This paper presents an adaptive mesh method for solving the Korteweg-de Vries-Burgers (KdVB) equation numerically. Ther-adaptive mesh method whichemploys 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 thevarious structures seen in these problems. Furthermore, it decreases the computationaleffort 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 thatemploying an adaptive moving mesh and a uniform mesh. By comparing the relativeerror for the obtained solutions of the problem, I will check the accuracy of the adaptive method.