探花 内射 L1 method for multi-singularity problems arising from time delay fractional equations (对于带多点奇异性的时代分数阶微分方程的L1数值算法)
发布日期：2024-12-23 04:22 点击次数：110
光华讲坛——社会绅士与企业家论坛第6697期探花 内射
主题：L1 method for multi-singularity problems arising from time delay fractional equations (对于带多点奇异性的时代分数阶微分方程的L1数值算法)
主讲东说念主：澳门大学数学系 黄锡荣庄重
主捏东说念主：数学学院 吕品庄重
时代：12月24日10:30探花 内射
方位：柳林校区通博楼B412会议室
控制单元：数学学院 科研处
主讲东说念主简介：
橾p在线黄锡荣，澳门大学数学系庄重，主要磋议鸿沟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。曾获多项澳门当然科学奖、担任SIAM东亚分会实际委员会委员和通知等。
实质摘要：
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.
本论述磋议的是分数阶延伸微分方程。咱们发现了该方程的解在延伸点s+处比在0+点处有更好的正则性弘扬。集中翻新的正则性表面，咱们磋议了一个安妥的L1数值算法。同期，咱们构建了一个具有最优的2-α阶的改良型L1算法探花 内射，并集中远大Laplace变换对相应算法进行了纰缪分析。