A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations (Advances in Applied Mathematics and Mechanics, 2023)
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) equationare examined as illustrative examples. Validity and accuracy of the proposed methodare assessed in terms of relative variance and the maximum error norm. Our resultsare found in good agreement with exact solutions and numerical solutions reported inprevious studies. Furthermore, it is found that the solution accuracy is closely relatedto the resolution level and the convergence-control parameter. It is also found that ourproposed method is superior to the traditional homotopy analysis method when dealing with unsteady nonlinear problems. It is expected that this approach can be furtherused to solve complicated unsteady problems in the fields of science and engineering.