报告题目：hp-error estimates of fractional collocation methods for Volterra integro-differential equations with weakly singular kernels

报告人：黄乘明教授

报告时间：2022年10月11日（本周二）19:30-22:30

#腾讯会议：121-660-371

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https://meeting.tencent.com/dm/MwBdeUKFkEru

摘要: In this talk, we propose an hp-version fractional collocation method for solving second kind Volterra integro-differential equations with weakly singular kernels. We derive hp-version error estimates in a weighted H1-norm for the method on arbitrary meshes. The results show that for any given mesh partition, exponential rates of convergence can be achieved for certain weakly singular solutions by linearly increasing the degrees of piecewise fractional polynomials. The results also imply that in the case of uniform mesh, the method has no (h-version) order barrier for weakly singular solutions, which is different from classical polynomial collocation methods. The method is easy to implement and has the same computational complexity as polynomial collocation methods. Numerical experiments are presented to demonstrate the efficiency of the proposed method.

个人简介：华中科技大学教授、博士生导师；主要从事微分方程数值计算研究，主持国家自然科学基金项目7项，参加国家自然科学基金重大研究计划重点项目1项；已在《SIAM Journal on Numerical Analysis》、《SIAM Journal on Scientific Computing》、《Numerische Mathematik》、《IMA Journal of Numerical Analysis》、《Journal of Computational Physics》等国内外学术期刊发表SCI论文100余篇；兼任中国数学会计算数学分会常务理事，湖北省计算数学学会副理事长，2005年入选教育部新世纪优秀人才支持计划，曾经或现任《Journal of Computational and Applied Mathematics》、《Journal of the Franklin Institute》、《PLOS ONE》、《Discrete Dynamics in Nature and Society》、《数值计算与计算机应用》等国内外期刊编委。