Abstract
In this paper, unconditionally optimal error estimates in L2-norm of two fully discrete schemes, one is backward Euler scheme and the other is a modified Crank-Nicolson scheme, are derived for cubic Schrödinger equation. Firstly, the mass and energy stability of the two schemes are proved rigorously. Secondly, the existence and uniqueness of the numerical solutions of the two schemes are presented. Based on the above priori estimations of the numerical solutions, unconditionally optimal error estimates in L2-norm are obtained without any timestep restrictions. Finally, some numerical results are provided to confirm the theoretical analysis.
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