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

The Coiflet wavelet-homotopy Galerkin method is extended to solve un-steady 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 deal-ing 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.