Abstract
This paper is devoted to the study of high-order finite difference scheme for the nonlinear Schrödinger equation with wave operator. The difference scheme is three level and a five point stencil is used for spatial variable. Existence of solutions is shown using a variant of Brouwer fixed point theorem. The unconditional stability as well as uniqueness of the difference scheme are also discussed in detail. The convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete maximum norm without any restrictions on the mesh sizes. Finally, some numerical experiments and comparisons with other existing methods in the literature are presented. The numerical results show that the high-order difference scheme of this article improves the accuracy of the space and time direction.
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