On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains

On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains

In this paper, we provide an explicit, stable and fast means to compute the approximate inverse of Hermite/Laguerre collocation differentiation matrices, and also the approximate inverse of the Hermite/Laguerre collocation matrices of a second-order differential operator. The latter offers optimal p...

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Bibliographic Details
Main Authors: Zhang, Chao, Wang, Li-Lian, Gu, Dongqin, Liu, Wenjie
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Mathematics
Hermite and Laguerre Differentiation Matrices
New Collocation Schemes
Online Access:https://hdl.handle.net/10356/141174
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Institution: Nanyang Technological University
Language: English
Description
Summary:In this paper, we provide an explicit, stable and fast means to compute the approximate inverse of Hermite/Laguerre collocation differentiation matrices, and also the approximate inverse of the Hermite/Laguerre collocation matrices of a second-order differential operator. The latter offers optimal preconditioners for developing well-conditioned Hermite/Laguerre collocation schemes. We apply the new approaches to various partial differential equations in unbounded domains and demonstrate the advantages over the usual collocation methods.

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