@article {5033,
	title = {A spectral solution of the Sturm-Liouville equation: comparison of classical and nonclassical basis sets},
	journal = {Journal of Computational and Applied Mathematics},
	volume = {136},
	number = {1-2},
	year = {2001},
	note = {ISI Document Delivery No.: 475METimes Cited: 16Cited Reference Count: 28},
	month = {Nov},
	pages = {17-35},
	type = {Article},
	abstract = {This paper considers a spectral method of solution of the Stunn-Liouville equation and the associated Schroedinger equation. The main objective is to develop a collocation method based on quadrature (collocation) points generated from nonclassical polynomials. The polynomials and associated quadrature points are calculated with Gautschi{\textquoteright}s Stieltjes procedure from some specified weight function. The particular spectral method used here with nonclassical basis sets is referred to as the Quadrature Discretization Method (QDM). The QDM and a related weighted QDM are applied to several Sturm-Liouville and Schroedinger equations and the results are compared with the traditional spectral methods based on Chebyshev and Legendre quadrature points. The results are also compared with the results of other workers wherever available. The QDM was found to give the most rapid convergence relative to other methods for the problems studied. (C) 2001 Elsevier Science B.V. All rights reserved.},
	keywords = {LAGRANGE, MESHES, METHOD QDM, nonclassical polynomials, NUMERICAL-INTEGRATION, ORTHOGONAL POLYNOMIALS, QUADRATURE DISCRETIZATION METHOD, SCHRODINGER-EQUATION, Schroedinger equation, spectral methods, Sturm-Liouville equation},
	isbn = {0377-0427},
	url = {<Go to ISI>://000171167400002},
	author = {Chen, H. and Shizgal, B. D.}
}
