報告題目：A New Collocation Scheme Using Non-polynomialBasis Functions
報告時間：2021年5月7日（星期五）15:30—17：00
報告地點：舜耕校區4號辦公樓3樓會議室
報告人：張超
主辦單位：數學與數量經濟學院
報告人簡介：
張超，江蘇師范大學數學與統計學院教授。2011在上海師范大學獲得理學博士學位，曾在新加坡南洋理工大學訪問。近年來，主持2項國家自然科學面上項目、1項江蘇省高校自然科學重大項目和1項江蘇省高等教育教改研究課題，在Mathematics of Computation、Journal of Scientific Computing等期刊上發表學術論文20余篇。現任江蘇省計算數學學會副理事長。
報告摘要：
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.
