A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator

Abstract In this paper, a compact finite difference scheme is presented for an periodic initial value problem of the nonlinear Schrodinger (NLS) equation with wave operator. This is a scheme of three levels with a discrete conservation law. The unconditional stability and convergence in maximum norm with order O ( h 4 + τ 2 ) are proved by the energy method. A numerical experiment is presented to support our theoretical results.

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