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In this paper, a new compact finite difference scheme is proposed for a periodic initial value problem of the nonlinear Schrödinger equation with wave operator. This is an explicit scheme of four levels with a discrete conservation law. The unconditional stability and convergence in maximum norm with order $$O(h^{4}+\tau ^{2})$$ O ( h 4 + τ 2 ) are verified by the energy method. Those...
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