Numerical solution of the 1-dimensional Burgers equation with splitting method derived for perturbed

In this thesis, the numerical solutions of the 1-dimensional Burgers equation obtained by splitting method based on implicit finite difference scheme have been analyzed in four chapter. In the first chapter, a brief review of the literature about 1-dimensional Burgers equation has been given. In the second chapter, some fundamental concepts, information about clasiccal finite difference methods and fixed point iteration have been presented. In the third chapter, Burgers equation has been introduced and the Fourier series solutions of the linearized Burgers equation for two different inital and boundary conditions have been given. Splitting methods obtained for perturbed system have been introduced. Additionally, the application of splitting method based on implicit finite difference scheme with filtering technique has been given. In the fourth chapter, the numerical solutions of Burgers equation with splitting method derived for perturbed system based on implicit finite difference scheme have been obtained . These solutions have been compared with their analytical solutions and some existing results in literature.