We study in this chapter spectral approximations by orthogonal polynomials/functions on unbounded intervals, such as Laguerre and Hermite polynomials /functions and rational functions. Considerable progress has been made in the last two decades in using these orthogonal systems for solving PDEs in unbounded domains (cf. Chap. 17 in Boyd (2001) and a more recent review article Shen and Wang (2009)).
KeywordsSpectral Method Unbounded Domain Hermite Polynomial Jacobi Polynomial Laguerre Polynomial
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