Numerical Solution of Some Class of Nonlinear Partial Differential Equations Using Wavelet-Based Full Approximation Scheme

Abstract

In the last decades, wavelets have become a dominant tool for having applications in almost all the areas of engineering and science such as numerical simulation of partial differential equations (PDEs). The performance of the conventional numerical methods has been found to involve some difficulty to observe fast convergence in low computational time. To overcome this difficulty, we presented wavelet-based full approximation scheme (WFAS) for the numerical solution of some class of nonlinear PDEs using Daubechies wavelet intergrid operators. The numerical results obtained by this scheme are compared with the exact solution to reveal the accuracy and also speed up convergence in lesser computational time as compared with the existing schemes. Some test problems are presented to show the applicability and attractiveness of WFAS.