Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains
This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This lea...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/101964 http://hdl.handle.net/10220/19843 |
| _version_ | 1811678252729630720 |
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| author | Shen, Jie Wang, Li-Lian Yu, Haijun |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Shen, Jie Wang, Li-Lian Yu, Haijun |
| author_sort | Shen, Jie |
| collection | NTU |
| description | This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This leads to particularly simple stiffness and mass matrices for higher-dimensional problems. The approximation results for both the usual tensor product space and hyperbolic cross space are established, with the latter particularly suitable for higher-dimensional problems. |
| first_indexed | 2024-10-01T02:50:19Z |
| format | Journal Article |
| id | ntu-10356/101964 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:50:19Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1019642023-02-28T19:43:37Z Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains Shen, Jie Wang, Li-Lian Yu, Haijun School of Physical and Mathematical Sciences DRNTU::Science::Mathematics This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This leads to particularly simple stiffness and mass matrices for higher-dimensional problems. The approximation results for both the usual tensor product space and hyperbolic cross space are established, with the latter particularly suitable for higher-dimensional problems. Accepted version 2014-06-20T07:14:59Z 2019-12-06T20:47:31Z 2014-06-20T07:14:59Z 2019-12-06T20:47:31Z 2013 2013 Journal Article Shen, J., Wang, L.-L., & Yu, H. (2014). Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. Journal of Computational and Applied Mathematics, 265, 264-275. 0377-0427 https://hdl.handle.net/10356/101964 http://hdl.handle.net/10220/19843 10.1016/j.cam.2013.09.024 en Journal of computational and applied mathematics © 2013 Elsevier B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Computational and Applied Mathematics, Elsevier B.V. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: http://dx.doi.org/10.1016/j.cam.2013.09.024]. 15 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Shen, Jie Wang, Li-Lian Yu, Haijun Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title | Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title_full | Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title_fullStr | Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title_full_unstemmed | Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title_short | Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains |
| title_sort | approximations by orthonormal mapped chebyshev functions for higher dimensional problems in unbounded domains |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/101964 http://hdl.handle.net/10220/19843 |
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