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.

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