An exponential spline solution of nonlinear Schrodinger equations with constant and variable coefficients

作者：Mohammadi Reza^*

来源：Computer Physics Communications, 2014, 185(3): 917-932.

DOI：10.1016/j.cpc.2013.12.015

• Nonlinear Schrodinger equation
• Gross-Pitaevskii equation
• Exponential spline
• Crank-Nicolson formulation
• Energy method
• Stability
• Convergence

In this study, the exponential spline scheme is implemented to find a numerical solution of the nonlinear Schrodinger equations with constant and variable coefficients. The method is based on the Crank-Nicolson formulation for time integration and exponential spline functions for space integration. The error analysis, existence, stability, uniqueness and convergence properties of the method are investigated using the energy method. We show that the method is unconditionally stable and accurate of orders O(k + kh + h(2)) and O(k + kh + h(4)). This method is tested on three examples by using the cubic nonlinear Schrodinger equation with constant and variable coefficients and the Gross-Pitaevskii equation. The computed results are compared wherever possible with those already available in the literature. The results show that the derived method is easily implemented and approximate the exact solution very well.

• 出版日期2014-3