报告题目 (Title): Variable-exponent Volterra integral equations and their use in fractional-derivative problems(变指数Volterra积分方程及其在分数阶导数问题中的应用)
报告人 (Speaker): Martin Stynes 教授（北京计算科学研究中心）
报告时间 (Time): 2021年10月19日(周二) 15:00
报告地点 (Place): 校本部G507
邀请人(Inviter): 李常品
报告摘要(Abstract): Piecewise polynomial collocation of weakly singular Volterra integral equations (VIEs) of the second kind has been extensively studied in the literature, where integral kernels of the form for some constant are considered. Variable-order fractional-derivative differential equations currently attract much research interest, and in Zheng and Wang SIAM J. Numer. Anal. 2020 such a problem is transformed to a weakly singular VIE whose kernel has the above form with variable , then solved numerically by piecewise linear collocation, but it is unclear whether this analysis could be extended to more general problems or to polynomials of higher degree. In the present paper the general theory (existence, uniqueness, regularity of solutions) of variable-exponent weakly singular VIEs is developed, then used to underpin an analysis of collocation methods where piecewise polynomials of any degree can be used. The sharpness of the theoretical error bounds obtained for the collocation methods is demonstrated by numerical examples.
报告人简介: Martin Stynes obtained his B.Sc and M.Sc. degrees from University College Cork, Ireland, then his PhD degree from Oregon State University, USA in 1977. After some other positions, he was at University College Cork from 1984 to 2012. Since 2013 he has been at Beijing CSRC, where he is a Chair Professor funded by the Chinese Government’s 1000 Talent Plan (Recruitment Program of Foreign Experts). He has worked for many years on the numerical solution of singularly perturbed differential equations; the book on this topic by Roos, Stynes and Tobiska is the standard international reference work (1st edition 1996, 2nd edition 2008). For the last 5 years he has worked mainly on fractional-derivative differential equations and their numerical solution. He is an editor of the journals Advances in Computational Mathematics, Applied Numerical Mathematics, and Computational Methods in Applied Mathematics.