Numerical solutions of KdV equation by using finite difference method

The main objective of this thesis is to obtain the numerical solutions of KdV eqution which has a quite importance in wave theory. For this objective, one of the basic numerical method, the finite difference method, is used. Some basic informations about waves are given in the first chapter. KdV equation and its related test problems are introduced in the second chapter. Finite difference formulas for the derivatives and some introductory informations about finite difference method are presented in the third chapter. Application of the numerical method for the KdV equation is constructed in the forth chapter. In the application of the numerical method, firstly, the time discretization of the equation is achieved by the help of Crank-Nicolson formulae. Then, the nonlinear terms in the equation are linearized by two different methods. A uniform partition of the solution domain is considered for the space discretization. The Thomas algorithm is used for the solutions of the obtained matrix equations. The numerical method is tested on different test problems. Accuracy of the method is investigated by error norms and the conservative laws of KdV equation. Finally, a conclusion is given in the last chapter.