报告人：李常品(上海大学数学系教授、博士生导师、伟长学者)
报告时间： 2024年05月14日(周二)上午9:00—12:00
报告地点：章辉楼442学术报告厅
联系人：陈雪娟副教授
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报告摘要：A novel H3N3-2σ interpolation approximation for the Caputo fractional derivative of order α∈(1, 2) is derived in this paper, which improves the popular L2C formula with (3-α)-order accuracy. By an interpolation technique, the second-order accuracy of the truncation error is skillfully estimated. Based on this formula, a finite difference scheme with second-order accuracy both in time and in space is constructed for the initial-boundary value problem of the time fractional hy-perbolic equation. It is well known that the coefficient properties of discrete fractional derivatives are fundamental to the numerical stability of time fractional differential models. We prove the related properties of the coefficients of the H3N3-2σ approximate formula. With these properties, the numerical stability and convergence of the difference scheme is derived immediately by the energy method in the sense of H1-norm. Considering the weak regularity of the solution to the problem at the starting time, a finite difference scheme on the graded meshes based on H3N3-2σ formula is also presented. The numerical simulations are performed to show the effectiveness of the derived finite difference schemes, in which the fast algorithms are employed to speed up the numerical computation.
报告人简介：上海大学数学系教授、博士生导师、伟长学者、Fellow of the Institute of Mathematics and its Applications, UK. 2021年获上海大学王宽诚育才奖，2017年和2010年获上海市自然科学奖，2016年入选上海市优秀博士学位论文指导教师，2012年获分数阶微积分领域的黎曼-刘维尔理论文章奖，2011年获宝钢优秀教师奖。主要研究方向为分数阶偏微分方程数值解。德国德古意特出版社系列丛书《Fractional Calculus in Applied Sciences and Engineering》创始主编，多个国际杂志编委。
理学院
2024年05月09日
