Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:265

Article

Shen, Jie^1,2  Wang, Li-Lian³  Yu, Haijun⁴ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

[4] Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC, AMSS, Beijing 100190, Peoples R China

关键词: Error estimates;    Spectral method;    Hyperbolic cross;    Higher-dimensional problems;    Unbounded domains.;    Mapped Chebyshev functions;   

DOI  :  10.1016/j.cam.2013.09.024

来源: Elsevier

【 摘 要 】

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. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free