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张超教授学术报告
发布时间:2018-06-29   浏览次数:  

报告题目:A new collocation scheme using non-polynomial basis functions

报告时间:201863016:00-17:00

报告地点:理学院120

报告人: 张超江苏师范大学教授,主要从事数值分析和科学计算方面研究工作

报告摘要: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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