2025年05月02日 星期五 登录 EN

学术活动
On the convergence of Galerkin methods for auto-convolution Volterra integral and integro-differential equations
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报告人:
Hui Liang, Professor, Harbin Institute of Technology, Shenzhen
邀请人:
Shipeng Mao, Professor
题目:
On the convergence of Galerkin methods for auto-convolution Volterra integral and integro-differential equations
时间地点:
10:00-11:00 May 9(Friday), S615
摘要:

The auto-convolution Volterra integral and integro-differential equations arise in many applications, for example, in the identification of memory kernels in the theory of viscoelasticity and in the computation of certain special functions. The convergence analysis of piecewise polynomial collocation solutions for these two kinds of equations is now largely well understood. However, the convergence analysis on Galerkin methods is still not clear. In this talk, we will show that the quadrature Galerkin method obtained from the Galerkin method by approximating the inner products by suitable numerical quadrature formulas, is equivalent to the continuous piecewise polynomial collocation method. In addition, the convergence and superconvergence of the numerical solution based on Galerkin methods are investigated.