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Discrete formulae for Caputo-Hadamard fractional derivatives and their applications in large time integration

主讲人：李常品

摘要：In this talk, three kinds of discrete formulas are proposed for approximating the Caputo–Hadamard fractional derivatives, which are called L1-2 formula, L2-1_{\sigma} formula, and H2N2 formula, respectively. Among them, the numerical formulas L1-2 and L2-1_{\sigma} are for order \alpha\in (0, 1) with (3−\alpha)-th order convergence, and H2N2 formula is for order \alpha\in (1, 2) with (3 − \alpha)-th order convergence too, where the theoretical convergence order has been verified by the illustrative examples. Finally, these three new formulas are applied to large time integration of fractional differential systems.

主讲人简介：李常品，现任上海大学理学院数学系教授、博士生导师，中国计算数学学会理事。主要研究方向为分数阶偏微分方程数值解、分岔混沌的应用理论和计算。李常品及其合作者在World Scientific编辑专著一部，在Chapman and Hall/CRC和SIAM出版专著各一部；发表SCI论文100余篇， ESI高被引论文12篇。主持国家自然科学基金、教育部留学回国人员科研启动基金、上海市教委科研创新重点项目等10余项，主持上海市教委本科重点课程建设项目、上海大学校级重点课程建设项目、思政专业课程“数值计算方法”建设项目和上海大学研究生创新培养项目《数值计算方法》各1项。是德国德古意特出版社系列丛书《Fractional Calculus in Applied Sciences and Engineering》的创始主编，是Applied Numerical Mathematics, Chaos, Fractional Calculus and Applied Analysis, International Journal of Bifurcation and Chaos, International Journal of Computer Mathematics, Journal of Nonlinear Science, Mathematics and Computers in Simulations等7种国际SCI杂志的副主编或编委，是《上海大学学报(自然科学版)》编委。

邀请人：李东方

时间：：2022年9月3日（星期六）10:00-12:30

地点：腾讯会议室     ID:643 391 895