Abstract
The fundamental idea behind spectral methods is to approximate solutions of PDEs by finite series of orthogonal functions such as the complex exponentials, Chebyshev, or Legendre polynomials. Chapter 1 reviews how to approximate functions, derivatives and integrals for both periodic and non-periodic problems using these series. It argues why and when these approximations converge rapidly in the number of degrees of freedom.
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© 2009 Springer Science + Business Media B.V.
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Kopriva, D.A. (2009). Spectral Approximation. In: Implementing Spectral Methods for Partial Differential Equations. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2261-5_1
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DOI: https://doi.org/10.1007/978-90-481-2261-5_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2260-8
Online ISBN: 978-90-481-2261-5
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