Compact Finite Difference Schemes With High Accuracy For One-dimensional Nonlinear Schrodinger Equation

摘要

In this paper, two compact finite difference schemes are presented for the numerical solution of the one-dimensional nonlinear Schroedinger equation. The discrete L_2-norm error estimates show that convergence rates of the present schemes are of order O(h~4 + τ~2). Numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy.