陈振荣学术报告预告
作者：张亚东 编辑：张燕 时间：2024-11-25 点击数：
报告题目：On the superconvergence of collocation methods based on two post-processing techniques for fractional integro-differential equations with weakly singular kernels
报告人： 陈振荣 博士
报告时间：2024年11月27日（星期三）16:30-18:00
腾讯会议ID：655 687 840
报告摘要：The purpose of this paper is to investigate the superconvergence of collocation methods for fractional integro-differential equations (FIDEs) with weakly singular kernels and Caputo derivative of order $0<\alpha<1$. First, the initial value problem of FIDEs is reformulated as a weakly singular Volterra integral equation (VIE), and the existence, uniqueness, and regularity of the exact solution for the original FIDE are obtained with the help of the resolvent theory of VIEs, and it is shown that the singularity of the exact solution is governed by the Caputo derivative, not the weakly singular kernel. Next, the piecewise polynomial collocation method is employed to solve the reformulated VIE numerically, and the optimal convergence order of the collocation solution is obtained on graded meshes. In order to improve the numerical accuracy, two types of postprocessing techniques are used--one is the classical iterated technique for VIEs and another one is the interpolation postprocessing technique. The superconvergence is thoroughly investigated and the optimal superconvergence orders are obtained for both of these two postprocessing techniques. Compared to the classical iterated collocation method, the interpolation postprocessing method has a lower calculation cost. The theoretical results are illustrated by numerical experiments.
个人简介: 陈振荣，博士。2022年12月获湘潭大学数学博士学位。2023年2月-至今，在哈尔滨工业大学（深圳）博士后助理研究员岗位工作。主要的研究方向为：偏微分方程、Volterra积分方程的数值解法。论文发表在BIT Numerical Mathematics, Journal of Computational Mathematics, Advances in Applied Mathematics and Mechanics等不同的国际杂志上。合著专著《Volterra型积分微分方程的谱方法》，即将在科学出版社出版。
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学科建设办公室 科研处 ok138cn太阳集团（应用数学研究所）
2024年11月25日
