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Spectral Methods for Partial Differential Equations,
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION HAMPTON VA LANGLEY RESEARCH CENTER
Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid-dynamical applications are emphasized.
This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983,' AD-A139 224, p883-925.