INVARIANTS-PRESERVING DU FORT-FRANKEL SCHEMES AND THEIR ANALYSES FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH WAVE OPERATOR  

作　　者：Dingwen Deng Zhijun Li 

机构地区：[1]College of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China

出　　处：《Journal of Computational Mathematics》2024年第3期814-850,共37页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11861047);by the Natural Science Foundation of Jiangxi Province for Distinguished Young Scientists(Grant No.20212ACB211006);by the Natural Science Foundation of Jiangxi Province(Grant No.20202BABL 201005).

摘　　要：Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stable scheme.However,there has been no research work on numerical solutions of nonlinear Schrödinger equations with wave operator by using Du Fort-Frankel-type finite difference methods(FDMs).In this study,a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional(1D)and two-dimensional(2D)nonlinear Schrödinger equations with wave operator.By using the discrete energy method,it is shown that their solutions possess the discrete energy and mass conservative laws,and conditionally converge to exact solutions with an order of for ofο(T^(2)+h_(x)^(2)+(T/h_(x))^(2))1D problem and an order ofο(T^(2)+h_(x)^(2)+h_(Y)^(2)+(T/h_(X))^(2)+(T/h_(y))^(2))for 2D problem in H1-norm.Here,τdenotes time-step size,while,hx and hy represent spatial meshsizes in x-and y-directions,respectively.Then,by introducing a stabilized term,a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised.They not only preserve the discrete energies and masses,but also own much better stability than original schemes.Finally,numerical results demonstrate the theoretical analyses.

关 键 词：Nonlinear Schrodinger equations with wave operator Du Fort-Frankel finite difference methods Discrete energy and mass conservative laws Numerical convergence 

分 类 号：O17[理学—数学]