报告题目：Spectral Collocation Methods Using Non-standard Basis Functions

报 告 人：张超教授（江苏师范大学）

报告时间：2022年12月15日  15:30

报告地点：腾讯会议（498163626）

报告摘要：

In this talk, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem. With a direct inverting the operator, the basis can be precomputed in a fast and stable manner. This leads to new collocation schemes for general second-order boundary value problems with (i) the matrix corresponding to the operator being identity; (ii) well-conditioned linear systems and (iii) exact imposition of various boundary conditions. This also provides efficient solvers for time-dependent nonlinear problems. Moreover, we can show that the new basis has the approximability to general functions in Sobolev spaces as good as orthogonal polynomials.

报告人简介：

张超，江苏师范大学教授，研究方向为偏微分方程数值解法，主要研究谱方法。近年来，主持2项国家自然科学基金面上项目、1项江苏省高校自然科学重大项目，在Mathematics of Computation、Joumal of Scientific Computing等期刊上发表学术研究论文20余篇，入选江苏省“333高层次人才培养工程”。现任江苏省计算数学分会副理事长。