Effective Mass and Energy Recovery by Conserved Compact Finite Difference Schemes

This paper is concerned with mass and energy recovery by some conserved compact finite difference schemes for the nonlinear Schrödinger-Poisson equations. The mass and energy conservation, the unique solvability, convergence and stability of the proposed schemes are proved. It is shown that the proposed methods are of order 2 in temporal direction and order 4 in spatial direction. Numerical experiments are presented to illustrate our theoretical results.