Abstract
The aim of this introductory chapter is to present, in a general way, the spectral methods in their various formulations: Galerkin, tau, and collocation. By using the notion of residual, it will be shown how spectral approximation can be defined for the representation of a given function as well as for the solution of a differential problem. These questions will be addressed in detail in the following two chapters devoted, respectively, to Fourier and Chebyshev methods.
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© 2002 Springer Science+Business Media New York
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Peyret, R. (2002). Fundamentals of spectral methods. In: Spectral Methods for Incompressible Viscous Flow. Applied Mathematical Sciences, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6557-1_2
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DOI: https://doi.org/10.1007/978-1-4757-6557-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2913-6
Online ISBN: 978-1-4757-6557-1
eBook Packages: Springer Book Archive