校庆65周年校友系列学术报告(2)-20210402
发布人:何杰  发布时间:2021-03-30   浏览次数:190

报告题目:A robust adaptive grid method for singularly perturbed delay Volterra integro-differential equations


刘利斌 博士

南宁师范大学

 


报告时间:202142(周五)  下15:30

地点:核工楼1216

 


摘要: In this talk, we study a nonlinear first-order singularly perturbed Volterra integro-differential equation with delay.  This equation is discretized by the backward Euler for differential part and the composite numerical quadrature formula for integral part for which  both an a priori and an a posteriori error analysis in the maximum norm are derived. Based on the a priori error bound and mesh equidistribution principle, we prove that there exists a mesh gives optimal first order convergence which is robust with respect to the perturbation parameter.  Then a posteriori error bound is used to choose a suitable monitor function and design a corresponding adaptive grid generation algorithm. Furthermore,  we extend our presented adaptive grid algorithm to a class of second-order nonlinear singularly perturbed delay differential equations. Numerical results are provided to demonstrate the effectiveness of our  presented monitor function. Meanwhile, it is shown that the standard arc-length monitor function is unsuitable for this type of singularly perturbed delay differential equations with a turning point.

 

 

 

报告专家简介:

刘利斌, 2005年本科毕业于东华理工大学理学院,2009年硕士毕业于广西民族大学,2015年博士毕业于华南师范大学数学科学学院。现为南宁师范大学数学与统计学院副教授,广西千名青年骨干教师,主要研究方向为微分方程数值解法及其应用,智能算法及其应用。主持完成国家自然科学基金项目3项、广西自然科学基金项目2项,作为核心成员参与广西自然科学基金重点项目2项。在国内外学术期刊发表学术论文40多篇;获得安徽省教学成果一等奖1.