On the Numerical Analysis of a Nonlinear Fractional Schrodinger Equation with Neumann Boundary Condition

Abstract

In the present paper, a nonlinear fractional Schrodinger equation is investigated with a numerical approach. First and second orders of accuracy difference schemes are constructed for a mixed problem for a nonlinear fractional Schrodinger equation with Neumann boundary condition. Results of numerical experiments support the convergence of solutions of constructed first and second order of accuracy difference schemes to exact solution of the problem.