報告題目：A new collocation scheme using non-polynomial basis functions
報告時間：2018年6月30日16:00-17:00
報告地點：必一体育平台120室
報告人: 張超，江蘇師範大學教授，主要從事數值分析和科學計算方面研究工作。
報告摘要:In this talk, we construct a set of non-polynomial basis functions from a generalized Birkhoff interpolation problem involving the operator: Lλ=d2/dx2−λ2 with constant λ. 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 Lλ 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。
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