Daubechies wavelet based full approximation scheme for solving Burgers'equation arising in Fluid Dynamics

Abstract

This \u00a0paper \u00a0presents, \u00a0Daubechies \u00a0wavelet \u00a0based \u00a0full \u00a0approximation \u00a0scheme \u00a0(DWFAS) \u00a0for \u00a0the numerical \u00a0solution \u00a0of \u00a0Burgers\u2019 \u00a0equation, \u00a0which \u00a0is \u00a0nonlinear \u00a0partial \u00a0differential \u00a0equation \u00a0(PDE) \u00a0arising \u00a0in fluid \u00a0dynamics \u00a0using \u00a0Daubechies \u00a0wavelet \u00a0intergrid \u00a0operartors. \u00a0The \u00a0numerical \u00a0solutions \u00a0obtained \u00a0are compared \u00a0with \u00a0existing \u00a0numerical \u00a0methods \u00a0and \u00a0exact \u00a0solution. \u00a0Some \u00a0of \u00a0the \u00a0test \u00a0problems \u00a0are \u00a0presented \u00a0to demonstrate that DWFAS has fast convergence in low computational time and is very effective, convenient and quite accurate to systems of PDEs.