Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrdinger equation
In this paper, two compact finite difference schemes are presented for the numerical solution of the one-dimensional nonlinear Schrdinger equation. The discrete L2 L 2 -norm error estimates show that convergence rates of the present schemes are of order O(h4+?2) O ( h 4 + ? 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.
65m06 35q55