The High-Order Compact Difference Scheme for Two-Dimensional Schr?dinger Equation
In this paper,the two-dimensional Schrödinger equation is split into two one-dimensional Schrödinger equations in x and y direction by using the local one-dimensional method.Then,the sixth-order compact scheme is used to deal with the second derivative terms of spatial variables,and the Schrödinger equation is transformed into a system of ordinary differential equations.The L-stable Simpson method is used to discretize the ordinary differential equation obtained from the space discretization.Therefore,a scheme with spatial sixth-order accuracy and temporal third-order accuracy is obtained,and the unconditional stability of the scheme is proved.Finally,the validity of the scheme is verified by numerical simulation and comparison.
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