讲座主题：The shifted convolution quadrature for fractional calculus and its applications

主讲人：刘洋

工作单位：内蒙古大学

讲座时间：2019年10月11日（周五）下午2:30

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

The convolution quadrature theory is a systematic approach to analyse the approximation of the Riemann-Liouville fractional operator. In this talk, we develop the shifted convolution quadrature (SCQ) theory which generalizes the theory of convolution quadrature by introducing a shifted parameter to cover as many numerical schemes. The constraint on the parameter is discussed in detail and the phenomenon of superconvergence for some schemes is examined from a new perspective. For some technique purposes when analysing the stability or convergence estimates of a method applied to PDEs, we design some novel formulas with desired properties under the framework of the SCQ. We conduct some numerical tests with nonsmooth solutions to further confirm our theory. Finally, a finite element method combined with the shifted convolution quadrature is developed and discussed.

主讲人介绍：

刘洋，内蒙古大学数学科学学院教授（博士）、博士生导师，现任中国计算数学学会理事。主要从事微分方程数值解法研究（有限元方法、混合有限元、间断Galerkin方法，尤其是分数阶微分方程数值方法）。目前发表多篇学术论文，其中SCI 40余篇，在国防工业出版社出版关于“偏微分方程的非标准混合有限元方法”专著一部。目前主持在研或结题2项国家自然科学基金、2项内蒙古自然科学基金和1项内蒙古自治区高校科学研究重点项目。