Wavelet Based Full Approximation Scheme for the Numerical Solution of Burgers’ equation arising in Fluid Dynamics using Biorthogonal wavelet

Abstract

Wavelet based methods are the new development in the area of applied mathematics. Wavelets are \u00a0mathematical \u00a0tools \u00a0that \u00a0cut \u00a0functions \u00a0or \u00a0operators \u00a0into \u00a0different \u00a0frequency \u00a0components, \u00a0and \u00a0then \u00a0study each \u00a0component \u00a0with \u00a0a \u00a0resolution \u00a0matching \u00a0to \u00a0its \u00a0scale. \u00a0In \u00a0this \u00a0paper, \u00a0we \u00a0proposed \u00a0Biorthogonal \u00a0wavelet based full-approximation scheme for the numerical solution of Burgers\u2019 equation arising in fluid dynamics using \u00a0biorthogonal \u00a0wavelet \u00a0filter \u00a0coefficients \u00a0as \u00a0prolongation \u00a0and \u00a0restriction \u00a0operators. \u00a0 \u00a0 \u00a0The \u00a0proposed method gives higher accuracy in terms of better convergence with low computational time, which has been demonstrated through the illustrative problem. \u00a0