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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sg-ntu-dr.10356-1411742020-06-04T09:10:43Z On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains Zhang, Chao Wang, Li-Lian Gu, Dongqin Liu, Wenjie School of Physical and Mathematical Sciences Science::Mathematics Hermite and Laguerre Differentiation Matrices New Collocation Schemes 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. MOE (Min. of Education, S’pore) 2020-06-04T09:10:41Z 2020-06-04T09:10:41Z 2018 Journal Article Zhang, C., Wang, L.-L., Gu, D., & Liu, W. (2018). On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains. Journal of Computational and Applied Mathematics, 344, 553-571. doi:10.1016/j.cam.2018.05.061 0377-0427 https://hdl.handle.net/10356/141174 10.1016/j.cam.2018.05.061 2-s2.0-85048879195 344 553 571 en Journal of Computational and Applied Mathematics © 2018 Elsevier B.V. All rights reserved. |
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Science::Mathematics Hermite and Laguerre Differentiation Matrices New Collocation Schemes |
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Science::Mathematics Hermite and Laguerre Differentiation Matrices New Collocation Schemes Zhang, Chao Wang, Li-Lian Gu, Dongqin Liu, Wenjie On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| description |
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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School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Zhang, Chao Wang, Li-Lian Gu, Dongqin Liu, Wenjie |
| format |
Article |
| author |
Zhang, Chao Wang, Li-Lian Gu, Dongqin Liu, Wenjie |
| author_sort |
Zhang, Chao |
| title |
On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| title_short |
On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| title_full |
On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| title_fullStr |
On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| title_full_unstemmed |
On approximate inverse of Hermite and Laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| title_sort |
on approximate inverse of hermite and laguerre collocation differentiation matrices and new collocation schemes in unbounded domains |
| publishDate |
2020 |
| url |
https://hdl.handle.net/10356/141174 |
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1681056383498190848 |