报告主题：Spectral Methods for Fractional Differential Equations
主讲人：许传矩
报告时间：2021年4月22日（周四）15:30—17：00
报告地点：舜耕校区4号楼学院会议室315
主办单位：数学与数量经济学院
主讲人简介：
许传炬，厦门大学数学科学学院特聘教授，博士生导师。1986年厦门大学本科毕业，1989年巴黎南大学硕士，1993年巴黎第六大学博士。研究领域包括: 计算流体谱元法，相场模型和算法，分数阶偏微分/积分方程的算法设计和分析，微分方程神经网络计算等。在有影响的学术期刊发表论文70多篇，研究成果被国际同行引用超3000多次。与国内外多所大学开展了合作，包括法国尼斯大学、波尔多大学、普瓦捷大学，美国普渡大学，新加坡国立大学和南洋理工大学等。担任多个国际学术期刊的编委，包括Communications on Applied Mathematics and Computation (2019 - present), SIAM Journal of Scientific Computing (2017 - present)，AIMS Mathematics (2016 - present)， Journal of Mathematical Study (2014 - present), Journal on Numerical Methods and Computer Applications (in Chinese, 2014 --- present), Discrete and Continuous Dynamical Systems - Series S (2013 - present)， East Asia Journal on Applied Mathematics (2011 - present), Numer. Math. J. Chinese Univ (2005 - present)等的编委。
报告摘要：
In this talk we will present two kinds of spectral methods for fractional differential equations.The first method make use of traditional polynomials for approximating fractional differential equations having regular solutionsThe second new method is constructed for a class of equations having solutions of low regularity.The new method makes use of fractional polynomials, also knownas Muntz polynomials. We first present some basic approximation properties of the Muntz polynomials, including error estimates for the weighted projection and interpolation operators. Then we will show how to constructefficient spectral methods by using the Muntz polynomials.A detailed convergence analysis will be provided.The potential application of the new method coversa large number of problems, including classical elliptic equations,integro-differential equations with weaklysingular kernels, fractional differential equations, and so on.