High-order structure-preserving Du Fort-Frankel schemesand their analyses for the nonlinear Schrödinger equation with wave operator

主讲人：邓定文

摘要：Du Fort-Frankel-type finite difference methods (DFFT-FDMs) are famous for good stability and easy implementation. In this study, by a perfect combination of the classical fourth-order difference to approximate the second-order spatial derivatives with the idea of DFFT-FDMs, a class of high-order structure- preserving DFFT-FDMs (SP-DFFT-FDMs) are firstly developed for solving the periodic initial-boundary value problems (PIBVPs) of 1D and 2D nonlinear Schrödinger equations with wave operator (NLSW), respectively. By using the discrete energy method, it is shown that their solutions satisfy the discrete energy- and mass- conservative laws, and are conditionally convergent. By supplementing a stabilized term, a type of stabilized SP-DFFT-FDMs are devised. They not only preserve the discrete energy- and mass- conservation laws, but also own much better stability than original SP-DFFT-FDMs.

主讲人简介：邓定文，博士，南昌航空大学数学与信息学院教授、硕士生导师, 江西省杰出青年基金获得者，主要从事偏微分方程有限差分法研究, 特别在紧致差分法、分裂算法和保结构算法等方面做出过有一定特色的研究工作，主持过国家自然科学基金项目3项及省厅级科研项目10项，获国家留学基金委面上项目资助访问加拿大约克大学1年，在 《Numerical Functional Analysis and Optimization》、《Applied Numerical Mathematics》、 《Applied Mathematical Modelling》等计算与应用数学刊物上发表科研论文40余篇。

邀请人：张诚坚

时间：2022年8月31日（星期三）21:00-23:00