A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator
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摘要
In this paper, a compact finite difference scheme is presented for an periodic initial value problem of the nonlinear Schrödinger (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(h4+τ2) are proved by the energy method. A numerical experiment is presented to support our theoretical results.
论文关键词:Nonlinear Schrödinger equation,Wave operator,Compact finite difference scheme,Convergence in maximum norm,Unconditional stability,Iterative algorithm
论文评审过程:Available online 18 October 2012.
论文官网地址:https://doi.org/10.1016/j.amc.2012.09.051