Wavelet based numerical solution of linear and non-linear parabolic partial differential equations using Lifting scheme

Abstract

Partial \u00a0differential \u00a0equations \u00a0are \u00a0fundamental \u00a0in \u00a0modeling \u00a0several \u00a0natural \u00a0phenomena. \u00a0The present work is designed for the Wavelet based numerical solution of linear and non-linear parabolic partial differential \u00a0equations \u00a0using \u00a0lifting \u00a0scheme. \u00a0To \u00a0demonstrate the \u00a0efficiency \u00a0and \u00a0competence \u00a0of \u00a0the \u00a0proposed scheme, we used \u00a0both orthogonal \u00a0and \u00a0biorthogonal wavelets. This \u00a0scheme speeds up convergence \u00a0in \u00a0lesser computational time as compared with existing schemes. Some test problems are presented for the validity and applicability of the scheme.