Time second‐order splitting conservative difference scheme for nonlinear fractional Schrödinger equation

Source abstract

This paper concentrates on the error estimation of novel time second‐order splitting conservative finite difference method (FDM) for high‐dimensional nonlinear fractional Schrödinger equation rigorously. The discrete preservation property of our scheme is exhibited. By virtue of the cut‐off technique and discrete energy method, it is shown that our scheme possesses the accuracy of in sense of ‐ norm. Numerical experiments are exhibited to validate the accuracy and conservation property of our scheme.