講座主題：The shifted convolution quadrature for fractional calculus and its applications
主講人：劉洋
工作單位：內蒙古大學
講座時間：2019年10月11日（周五）下午2:30
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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 con?rm our theory. Finally, a finite element method combined with the shifted convolution quadrature is developed and discussed.
主講人介紹：
劉洋，內蒙古大學數學科學學院教授（博士）、博士生導師，現任中國計算數學學會理事。主要從事微分方程數值解法研究（有限元方法、混合有限元、間斷Galerkin方法，尤其是分數階微分方程數值方法）。目前發表多篇學術論文，其中SCI 40余篇，在國防工業出版社出版關于“偏微分方程的非標準混合有限元方法”專著一部。目前主持在研或結題2項國家自然科學基金、2項內蒙古自然科學基金和1項內蒙古自治區高校科學研究重點項目。
