Numerical solutions of Schrödinger equation

The main objective of this thesis is to obtain the numerical solutions of the time dependent nonlinear cubic Schrödinger eqution which has a quite importance in the literature. For this objective, nonpolynomial cubic spline interpolation is used. Some basic informations about wave theory and Schrödinger equation are given in the first chapter. Spline functions are introduced in the second chapter. Application of the numerical method and calculation of the results are presented in the third chapter. A conclusion with the obtained results is given in the last chapter. In the application of the numerical method, firstly, the time discretization of the equation is achieved by the help of forward difference formula. A uniform partition of the solution domain is considered for the space discretization. Appropriate determination of the parameters that appeared in the cubic spline relation is achived by calculating the local truncation error. By using von-Neumann technique, it is shown that the method is unconditionally stable. Finally, the numerical method is tested on two problems. Keywords: Wave, Schrödinger, Soliton, Spline.