Preconditioning of spectral methods via Birkhoff interpolation

被引：0
作者：
Conor McCoid
Manfred R. Trummer
机构：
[1] Simon Fraser University,Department of Mathematics
来源：
Numerical Algorithms | 2018年 / 79卷
关键词：
Two-point boundary value problems; Spectral methods; Preconditioning; Birkhoff interpolation; 65N35; 65L10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
High-order differentiation matrices as calculated in spectral collocation methods usually include a large round-off error and have a large condition number (Baltensperger and Berrut Computers and Mathematics with Applications 37(1), 41–48 1999; Baltensperger and Trummer SIAM J. Sci. Comput. 24(5), 1465–1487 2003; Costa and Don Appl. Numer. Math. 33(1), 151–159 2000). Wang et al. (Wang et al. SIAM J. Sci. Comput. 36(3), A907–A929 2014) present a method to precondition these matrices using Birkhoff interpolation. We generalize this method for all orders and boundary conditions and allowing arbitrary rows of the system matrix to be replaced by the boundary conditions. The preconditioner is an exact inverse of the highest-order differentiation matrix in the equation; thus, its product with that matrix can be replaced by the identity matrix. We show the benefits of the method for high-order differential equations. These include improved condition number and, more importantly, higher accuracy of solutions compared to other methods.
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页码：555 / 573
页数：18
相关论文
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