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 - <p style="text-align: justify;">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.</p>