A New Collocation Scheme Using Non-polynomial Basis Functions

作者：Zhang, Chao; Liu, Wenjie; Wang, Li-Lian^*

来源：Journal of Scientific Computing, 2017, 70(2): 793-818.

DOI：10.1007/s10915-016-0269-7

• Generalised Birkhoff interpolation problem
• Non-polynomial basis
• Well-conditioned collocation methods

In this paper, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem involving the operator: with constant 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 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.

• 出版日期2017-2
• 单位哈尔滨工业大学; 南阳理工学院