On the numerical solution of Burgers equation with Galerkin method

This study, which is prepared as a master thesis, consists of five chapters. In the first chapter, the basic concepts which will be used in the following chapters are given. In the second chapter, the information about residual weighted method are given. In the third chapter, the global matrices which are used in the computation obtained for study are also given. After the heat equation is introduced, literature review of the equation is presented. Cubic B-spline Galerkin method applied to the heat equation and the martices are also given which are used in the computation obtained for study. In addition, numerical solutions for the heat equation given with different initial and boundary conditions are evaluated and these solutions are compared with other studies. A von Neumann stability analysis of the method is also investigated. In the fourth chapter, Hopf-Cole transformation is applied to the Burgers Equation, after the equation is transformed into linear heat equation, cubic B-spline Galerkin method is applied to equation and numerical solutions is gained from equation. The obtained numerical solutions are given in the tables and these comptued results are compared with other numerical solution in the literature. In the fifth chapter, the results obtained in the fourth chapter have been briefly evaluated.