講座主題：Volterra積分方程的分數階配置方法
主講人：蔡好濤
工作單位：山東財經大學
講座時間：2019年10月11日（周五）下午4:30
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
蔡好濤，理學博士，博士后，現為山東財經大學數學與數量經濟學院教授。近年來獨立或第一作者在《SIAM Journal on Numerical Analysis》、《Journal of Scientific Computing》、《Applied Numerical mathematics》、《Journal of Complexity》、《BIT： Numerical mathematics》等計算數學領域發表論文20余篇，主持并完成一項國家自然科學基金項目，兩項山東省自然科學基金項目和一項中國博士后基金項目，兩次入選山東財經大學優秀青年人才支持計劃。
