讲座主题：Volterra积分方程的分数阶配置方法

主讲人：蔡好涛

工作单位：山东财经大学

讲座时间：2019年10月11日（周五）下午4:30

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

The classical integer-order Jacobi spectral methods for solving second kind nonlinear Volterra integral equations with weakly singular kernels may cause a low-order accuracy in numerically approximating the exact solution. To overcome the shortcomings, we in this paper present a fractional spectral collocation method for solving weakly singular nonlinear Volterra integral equations. Based on the behavior of the original solution near the initial point of integration, we construct the fractional interpolation basis in the collocation method, and then develop an easily implementing technique to approximate the entry with one-fold integral in the resulting nonlinear system produced by the fractional spectral method. Consequently, we establish that both the semi-discrete and the fully discrete nonlinear systems have a unique solution for sufficiently large $n$, respectively, where $n+1$ denotes the dimension of the approximate space. We also ensure that two approximate solutions produced by both the semi-discrete and the fully discrete method arrive at the quasi-optimal convergence order in the infinite norm. At last, numerical examples are given to confirm the theoretical results.

主讲人介绍：

蔡好涛，理学博士，博士后，现为山东财经大学数学与数量经济学院教授。近年来独立或第一作者在《SIAM Journal on Numerical Analysis》、《Journal of Scientific Computing》、《Applied Numerical mathematics》、《Journal of Complexity》、《BIT： Numerical mathematics》等计算数学领域发表论文20余篇，主持并完成一项国家自然科学基金项目，两项山东省自然科学基金项目和一项中国博士后基金项目，两次入选山东财经大学优秀青年人才支持计划。