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A New Collocation Scheme Using Non-polynomial Basis Functions
2021-05-06 08:52 Read:

Topic:A New Collocation Scheme Using Non-Polynomial Basis Functions

Time:15:30-17:00, May 7 (Friday), 2021

Place:Meeting room on the 3rdfloor, 4thadministrative building, Shungeng Campus

Speaker:Zhang Chao

Hosted by:School of Mathematics and Quantitative Economics

Introduction to the Speaker:

Zhang Chao, Professor of School of Mathematics and Statistics, Jiangsu Normal University, received Doctor of Science in Shanghai Normal University in 2011 and paid an academic visit to Nanyang Technological University, Singapore. Professor Zhang presides overtwoGeneral Programs of the National Natural Science Foundation of China, a major project of College Natural Science Program of Jiangsu Province,and a Research Topic on Teaching Reform of Jiangsu Higher Education. Professor Zhang has published over 20 papersinacademic journals asMathematics of Computation,Journal of Scientific Computing. Professor Zhang now holds a post as vice president of Jiangsu Mathematical Society.

Abstract of the Lecture:

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

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