勷勤数学•专家报告

题      目：Numerical study on time delay fractional differential equations

报  告  人：黄锡荣 教授  (邀请人：陈小山)

                                              澳门大学       

时      间：4月21日  10：20-11：20

地     点：数科院东楼401

报告人简介:

        黄锡荣，博士，澳门大学科技学院博导，教授。主要研究方向：数值线性代数、数值微分方程、优化与控制论等领域。在SIAM Journal on Matrix analysis and Applications.、Journal of Differential Equations、Journal of Computational Physics等期刊发表学术论文120余篇。研究成果分别获2016年和2022年澳门自然科学奖二等奖和三等奖。

摘      要：

      In this talk, we study delay fractional equations. We show that that the regularity of the solution at s+ is better than that at 0+, where s is a constant time delay. Improved regularity of the solution is obtained by the decomposition technique and a fitted L1 numerical scheme is designed for it. We then construct a corrected L1 scheme, of which optimal convergence order reaches 2 - α, where α∈(0, 1) is the order of the Caputo derivative. Significantly, the correction terms share the same forms as the discrete convolution structure for the derivative, which implies that the computation and analysis of these two parts can be integrated together. Finally, error pointwise estimates of L1 method for delay fractional equations are derived by discrete Laplace transform method. 

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