主题：L1 method for multi-singularity problems arising from time delay fractional equations (关于带多点奇异性的时间分数阶微分方程的L1数值算法)

主讲人：澳门大学数学系 黄锡荣教授

主持人：数学学院  吕品教授

时间：2024年12月24日（周二）10:30

地点：柳林校区通博楼B412会议室

主办单位：数学学院  科研处

主讲人简介：

黄锡荣，澳门大学数学系教授，主要研究领域为偏微分方程数值解和数值代数。在SIMAX、JCP、JSC、JDE等知名SCI期刊上发表100余篇论文。曾获多项澳门自然科学奖、担任SIAM东亚分会执行委员会委员和秘书等。

内容提要：

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.

本报告讨论的是分数阶延迟微分方程。我们发现了该方程的解在延迟点s+处比在0+点处有更好的正则性表现。结合改进的正则性理论，我们研究了一个恰当的L1数值算法。同时，我们构建了一个具有最优的2-α阶的校正型L1算法，并结合离散Laplace变换对相应算法进行了误差分析。