10月24日 汕头大学林福荣教授学术报告

发布时间:2019-10-21   浏览次数:11

报 告 人: 林福荣 教授(汕头大学)

报告题目:Crank-Nicolson-weighted-shifted-Grunwald-difference schemes for space Riesz variable-order fractional diffusion equations

报告时间:2019年10月24日(周四)上午10:00—11:00

报告地点:静远楼1508学术报告厅

报告人简介:

林福荣,香港大学博士, 汕头大学数学系教授, 博士生导师. 1985 年7 月、1988年7月分别毕业于复旦大学数学系和数学所, 获学士和硕士学位;1995 年9 月毕业于香港大学数学系, 获博士学位. 1988年到汕头大学数学系工作, 2002年晋升为教授. 先后获得汕头市优秀教师、汕头市十佳青年科技带头人、汕头市劳动模范、南粤优秀教师和广东省五一劳动奖章等荣誉. 主要研究领域包括积分方程快速求解、Toeplitz方程组快速求解和分数阶微分方程的离散方法与快速算法等. 多次到港澳, 新加坡和美国等地进行学术访问和合作. 先后分别主持国家自然科学基金4 项, 广东省自然科学基金项目3 项. 发表论文50 余篇, 其中30 多篇论文发表在``SIAM J. Numerical Analysis'', ``SIAM J. Scientific Computing'', ``Inverse Problems'', ``Numerical Linear Algebra with Applications'', ``BIT'', ``Advances in Computational Mathematics'', ``Applied Numerical Mathematics'', ``Journal of Computational Physics'' 等SCI 收录的杂志上.

报告摘要:

In this talk, high precision difference schemes are proposed to solve the initial-boundary value problem for space Riesz variable-order fractional diffusion equations. Based on weighted-shifted-Grunwald-difference (WSGD) operators proposed in [Journal of Computational and Applied Mathematics 363 (2020) 77-91] for Riemann-Liouville fractional derivatives, we derive WSGD operators for variable-order ones by using the relation between variable-order fractional derivative and (invariable-order) fractional derivative. We then apply Crank-Nicolson-weighted-shifted-Grunwald-difference (CN-WSGD) schemes to the initial-boundary problem for space Riesz variable-order diffusion equations. Theoretical results on the stability of CN-WSGD schemes are presented and proved. Moreover, we derive a problem-based method to choose suitable CN-WSGD schemes which leads to unconditioned stable linear systems with optimal upper bound for accuracy. Numerical results show that the proposed schemes are very efficient.