报告人：邓定文（南昌航空大学）

邀请人：张诚坚

报告时间：2023年8月18日（星期五）14:30-16:30

报告地点：科技楼南楼813室

报告题目：A class of weighted energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon-type equations

报告摘要：Recently, invariant energy-quadratization methods (IEQMs) have been introduced by Xiaofeng Yang'sgroup to develop linear and energy-dissipation-preserving methodsfor nonlinear energy-dissipation systems. Following their work, two auxiliary functions are firstly introduced to rewritethe sine-Gordon equation (SGE) and coupled sine-Gordon equations (CSGEs) into equivalent systems, respectively. Then, two energy-preserving Du Fort-Frankel-type finite difference methods (EP-DFFT-FDMs) have been suggested for them, respectively. By using the discrete energy methods, the discrete energy conservative laws and convergence rates in the  -norm have been derived, rigorously. It is worth mentioning that the proposed discrete energy is an approximation to the exact energy of the continuous problem. As  ,   and parameter   1/4, the current methods are stable in the  -norm because numerical solutions obtained by them are bounded in the  -norm. What's more,as parameter   1/4, the current methods are unconditionally stable in the -norm because numerical solutions obtained by them are uniformly bounded in the  -norm. Moreover, our methods are explicit, and very easy to be implemented. However, a shortcoming of the current methods is that they are conditionally consistent. Namely,   and  tend to zero as time step  , spatial meshsizes   in  -direction and   in  -direction tend to zero. Numerical findings support the correctness of theoretical analyses and the performance of the algorithms.

报告人简介：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.