报告题目：A New Collocation Scheme Using Non-polynomialBasis Functions

报告时间：2021年5月7日（星期五）15:30—17：00

报告地点：舜耕校区4号办公楼3楼会议室

报告人：张超

主办单位：数学与数量经济学院

报告人简介：

    张超，江苏师范大学数学与统计学院教授。2011在上海师范大学获得理学博士学位，曾在新加坡南洋理工大学访问。近年来，主持2项国家自然科学面上项目、1项江苏省高校自然科学重大项目和1项江苏省高等教育教改研究课题，在Mathematics of Computation、Journal of Scientific Computing等期刊上发表学术论文20余篇。现任江苏省计算数学学会副理事长。

报告摘要：

In this paper, we construct a set of non-polynomial basis functions from a generalisedBirkhoff interpolation problem involving the operator: L_\lambda={d^2}/{dx^2}-\lambda^2 with constant \lambda. With a direct inverting the operator, the basis can be pre-computed 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 L_\lambda 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 theapproximability to general functions in Sobolev spaces as good as orthogonal polynomials.