New wavelet based full-approximation scheme for the numerical solution of nonlinear elliptic partial differential equations

Abstract

Recently, wavelet analysis application has dragged the attention of researchers in a wide variety of practical problems, particularly for the numerical solution of nonlinear partial differential equations. Based on Daubechies filter coefficients, a modified method using wavelet intergrid operators known as new wavelet based full-approximation scheme (NWFAS) similar to multigrid full-approximation scheme (FAS) is developed for the numerical solution of nonlinear elliptic partial differential equations. The present method gives higher accuracy in terms of better convergence with low CPU time. The results of tested examples of proposed method show better performance which is demonstrated through the illustrative examples.