Abstract : In this thesis modeling of Burger's equation, Fisher's equation and finally generalized Burger-Fisher equation is discussed. Analytical and numerical methods to solve this equation by other authors have been quoted. Galerkin method is used to solve this equation. Efficient, accurate and well-conditioned algorithms are developed and implemented. Numerical results shows that Galerkin method gives better convergence which has also been proved analytically. Remarks have been given to attempt Galerkin method on the higher dimensions of this equation.