A Four Step Wavelet Galerkin Method for Parabolic and Hyperbolic Problems

In this paper a four step wavelet based higher order Taylor Galerkin methods is given in this study. The method is fourth order accurate in time and O (2^ (-jp)) give the accuracy in space. In contrast with the Taylor-Galerkin method the present four step finite element method lacks any new high order derivatives andis suitable for solving non-linear problems. The concisely supported orthogonal wavelet bases developed by Daubechies are used in Galerkin method. The behavior of the given method is applicable both parabolic and hyperbolic partial differential equation.