Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions

  • Authors:

  • Jie Shen

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 2000

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Abstract

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.