应002全讯白菜网数学系赵景军教授的邀请，2017年5月3日 上午9：00-10：00在格物楼503，上海大学李常品教授来访数学系并做学术报告。报告题目：Finite difference methods with non-uniform meshes for FDEs，报告由赵景军教授主持，数学系20余位师生听取了报告，并进行了热烈的讨论。

报告摘要：

Generally speaking, the fractional differential equations (FDEs) are quite different from the integer-order differential equations. For the former, even if the resource item and the initial/boundary value conditions are smooth enough, the solutions of the corresponding equations can be non-smooth. On the other hand, for the given fractional differential equations, even if the resource item and the initial/boundary value conditions are non-smooth in the given domain, their solutions can be smooth enough in the same domain. These mean that poor convergent rate may be obtained if uniform meshes are used.

In this talk, finite difference methods with non-uniform meshes for solving nonlinear FDEs are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.

个人简介：

李常品：上海大学数学系教授、博士生导师。研究兴趣：分数阶偏微分方程数值解、分数阶动力学。在SIAM Journals、J Comput Phys、PRE、Phys D、Chaos等杂志上发表100余篇文章，SCI他引近3000次；在世界科学出版社编辑出版专著1部，在CRC出版社出版专著1部。先后应邀访问南非、新加坡、美国、澳大利亚等国的多所大学。现任Fractional Calculus and Applied Analysis、Int J Comput Math、Int J Bifurcation Chaos、Chaos等SCI杂志的编委或顾问委员会成员。 2010年获上海市自然科学奖，2011年获宝钢优秀教师奖，2012年获最佳黎曼-刘维尔理论文章奖，2016年获“2015年度科学中国人”称号，2016年入选中国高被引学者榜单。