A nonstandard finite difference method for solving Schrodinger equation

In this work, by introducing a transformation, the nonlinear Schrodinger equation is converted to anordinary differential equation (ODE). Then, two nonstandard finite difference (NSFD) schemes are constructedfor studying the reduced equation. Finally, the results of the methods are compared with each other and alsowith the results of the standard finite difference scheme at some points. The graphs of the errors of numericalsolutions for these schemes are plotted and compared with the exact solutions.

Keywords:

Schrodinger equation , finite difference , nonstandard scheme