Numerical solution of fractional coupled nonlinear Schrödinger equation systems

In this thesis, numerical solutions of fractional nonlinear Schrödinger equation systems are evaluated by using a meshless method based on radial basis function collocation method. These equations are TSFCNLS, CNLS, TFCNLS and SFCNLS. Various test problems are used to demonstrate the validity of the suggested method. There are no exact solutions of the TSFCNLS, TFCNLS and SFCNLS equations in the literature. For this reason, an error estimates method is used and computed numerical solutions for the selected fixed time and space step size are accepted as reference solutions. Then, the computed numerical solutions for larger time and step size are compared with these reference solutions and the error norms in terms of L_{\infty} are calculated. For the single soliton solution of the CNLS equation whose analytic solution is known L_2, L_\infty error norms and the values of conservation are calculated for each test problem. In addition, obtained numerical results for each equation are illustrated by tables and figures. Finally, stability analysis of the difference equation obtained by the RBFC method for TSFCNLS equation is examined by the Von-Neumann stability method and stability analysis results of other equations are obtained from the stability analysis outcome of TSFCNLS.