Open AccessStable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
Author(s) -
Jie Shen
Publication year - 2000
Publication title -
siam journal on numerical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.78
H-Index - 134
eISSN - 1095-7170
pISSN - 0036-1429
DOI - 10.1137/s0036142999362936
Subject(s) - laguerre polynomials , mathematics , sobolev space , spectral method , laguerre's method , galerkin method , convergence (economics) , rate of convergence , mathematical analysis , spectral analysis , orthogonal polynomials , finite element method , computer science , classical orthogonal polynomials , computer network , channel (broadcasting) , physics , economics , thermodynamics , economic growth , quantum mechanics , spectroscopy
Stable and efficient spectral methods using Laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains. It is shown that spectral-Galerkin approximations based on Laguerre functions are stable and convergent with spectral accuracy in the usual (not weighted) Sobolev spaces. Efficient, accurate, and well-conditioned algorithms using Laguerre functions are developed and implemented. Numerical results indicating the spectral convergence rate and effectiveness of these algorithms are presented.
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