Solution of the burgers' equation with exponential finite difference methods

This thesis consists of four chapters. In the first chapter, a review of the literature with the Burgers' equation and exponential finite difference method is given. In the second chapter, Hopf-Cole transformation is used to linearize Burgers' equation and model problems are used to test the presented methods. The third and fourth chapters of the thesis are the original parts. In the third chapter, Burgers' equation linearized by Hopf-Cole transformation is solved with explicit, implicit and Crank-Nicolson exponential finite difference methods. These solutions are compared with analytical solutions. Also, the results are analyzed by plotted three-dimensional graphs. In the fourth chapter, solutions are obtained by implicit, fully implicit and Crank-Nicolson exponential finite-difference methods applied directly to the Burgers' equation. The comparisons of numerical solutions with analytical solutions are presented in the tables.