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This paper is concerned with mass and energy recovery by some conserved compact finite difference schemes for the nonlinear Schro&#x0308;dinger-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.

Effective Mass and Energy Recovery by Conserved Compact Finite Difference Schemes