Approximate solution of a linear and a nonlinear parabolic problems by Galerkin method

In this study, we investigate the weak solutions of linear and nonlinear parabolic problems subject to Dicihlet boundary conditions. Using Galerkin method and Adomian method approximate solutions of these problems have been obtained. Appling the Galerkin method to linear parabolic problems, the system of linear ordinary differential equations has been get. Using the Galerkin method to nonlinear parabolic problems, we have the system of nonlinear ordinary differential equations. Adomian decomposition method to solve these systems of the ordinary differential equations has been used. Obtained results are tested with some numerical examples by using MAPLE® program.