@Article{AAMM-15-964,
author = {Zhou , Yue and Xu , Hang},
title = {A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {4},
pages = {964--983},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0046},
url = {http://global-sci.org/intro/article_detail/aamm/21598.html}
}