Crank-Nicolson implicit method for the nonlinear Schrodinger equation with variable coefficient

Abstract

In the present work, the Crank-Nicolson implicit scheme for the numerical solution of nonlinear Schrodinger equation with variable coefficient is introduced. The Crank-Nicolson scheme is second order accurate in time and space directions. The stability analysis for the Crank-Nicolson method is investigated and this method is shown to be unconditionally stable. The numerical results obtained by the Crank-Nicolson method are presented to confirm the analytical results for the progressive wave solution of nonlinear Schrodinger equation with variable coefficient. © 2014 AIP Publishing LLC.