Solution of two dimensional burgers equation by alternating direction implicit (Adi) method

This thesis consists of seven chapters. In the first chapter, short history of the Alternating Direction Implicit (ADI) method is presented. In the second chapter, finite difference approaches to derivatives, finite difference methods and von Neumann stability analysis method are presented. In the third chapter, seven model problems which are considered in this thesis and the methods which are used to obtain the numerical solutions of this model problems are presented. In the fourth chapter, by considering the relation between the system of two dimensional Burgers equations and Hopf-Cole transformation the exact solutions of the system of two dimensional Burgers equations are given. Chapter 5 and chapter 6 are the original part of this thesis. In the fifth chapter, Alternating Direction Implicit (ADI) approximations of two dimensional heat equation, two dimensional Burgers equation and the system of two dimensional Burgers equations are given. Also stability analysis of given approximations are investigated with von Neumann stability analysis method. In the sixth chapter, numerical solutions of model problems are obtained by using ADI method. Obtained numerical solutions are compared with exact solutions and numerical solutions that were obtained in other studies in the literature by presenting tables and graphs. Chapter 7 is the part of conclusion and discussion.