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Volume 23, Issue 2
Generalized Laguerre Approximation and Its Applications to Exterior Problems

Ben-Yu Guo, Jie Shen & Cheng-Long Xu

J. Comp. Math., 23 (2005), pp. 113-130.

Published online: 2005-04

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  • Abstract

Approximations using the generalized Laguerre polynomials are investigated in this paper. Error estimates for various orthogonal projections are established. These estimates generalize and improve previously published results on the Laguerre approximations. As an example of applications, a mixed Laguerre-Fourier spectral method for the Helmholtz equation in an exterior domain is analyzed and implemented. The proposed method enjoys optimal error estimates, and with suitable basis functions, leads to a sparse and symmetric linear system.

  • Keywords

Generalized Laguerre polynomials, Exterior problems, Mixed Laguerre-Fourier spectral method.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-113, author = {Ben-Yu Guo, Jie Shen and Cheng-Long Xu}, title = {Generalized Laguerre Approximation and Its Applications to Exterior Problems}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {2}, pages = {113--130}, abstract = {

Approximations using the generalized Laguerre polynomials are investigated in this paper. Error estimates for various orthogonal projections are established. These estimates generalize and improve previously published results on the Laguerre approximations. As an example of applications, a mixed Laguerre-Fourier spectral method for the Helmholtz equation in an exterior domain is analyzed and implemented. The proposed method enjoys optimal error estimates, and with suitable basis functions, leads to a sparse and symmetric linear system.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8801.html} }
TY - JOUR T1 - Generalized Laguerre Approximation and Its Applications to Exterior Problems AU - Ben-Yu Guo, Jie Shen & Cheng-Long Xu JO - Journal of Computational Mathematics VL - 2 SP - 113 EP - 130 PY - 2005 DA - 2005/04 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8801.html KW - Generalized Laguerre polynomials, Exterior problems, Mixed Laguerre-Fourier spectral method. AB -

Approximations using the generalized Laguerre polynomials are investigated in this paper. Error estimates for various orthogonal projections are established. These estimates generalize and improve previously published results on the Laguerre approximations. As an example of applications, a mixed Laguerre-Fourier spectral method for the Helmholtz equation in an exterior domain is analyzed and implemented. The proposed method enjoys optimal error estimates, and with suitable basis functions, leads to a sparse and symmetric linear system.

Ben-Yu Guo, Jie Shen and Cheng-Long Xu. (2005). Generalized Laguerre Approximation and Its Applications to Exterior Problems. Journal of Computational Mathematics. 23 (2). 113-130. doi:
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