A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations

A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations

Year:    2023

Author:    Yue Zhou, Hang Xu

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 964–983

Abstract

The Coiflet wavelet-homotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time. The Korteweg-de Vries (KdV) equation, the Burgers equation and the Korteweg-de Vries-Burgers (KdVB) equation are examined as illustrative examples. Validity and accuracy of the proposed method are assessed in terms of relative variance and the maximum error norm. Our results are found in good agreement with exact solutions and numerical solutions reported in previous studies. Furthermore, it is found that the solution accuracy is closely related to the resolution level and the convergence-control parameter. It is also found that our proposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear problems. It is expected that this approach can be further used to solve complicated unsteady problems in the fields of science and engineering.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0046

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 964–983

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Coiflet wavelet homotopy analysis method wavelet-homotopy method wave equations unsteady.

Author Details

Yue Zhou

Hang Xu