Abstract
Spectral methods for solving differential equations of boundary value type have traditionally been based on classical orthogonal polynomials such as the Chebyshev, Legendre, Laguerre, and Hermite polynomials. In this numerical study we show that methods based on nonclassical orthogonal polynomials may sometimes be more accurate. Examples include the solution of a two-point boundary value problem with a steep boundary layer and two Sturm-Liouville problems.
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Weideman, J.A.C. (1999). Spectral Methods Based on Nonclassical Orthogonal Polynomials. In: Gautschi, W., Opfer, G., Golub, G.H. (eds) Applications and Computation of Orthogonal Polynomials. International Series of Numerical Mathematics, vol 131. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8685-7_18
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DOI: https://doi.org/10.1007/978-3-0348-8685-7_18
Publisher Name: Birkhäuser, Basel
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