Abstract
In this chapter we design and examine trigonometric collocation methods for the same integral equation Au = f as in Chapter 9. We consider only the schemes where the collocation method is applied directly to the equation without a preconditioning of it. A full discretization is achieved using a kind of product integration. This leads to more simple and straightforward discretization schemes than by the Galerkin method. On the other hand, the justification of the methods is more complicated and some open problems remain. Of course, the collocation method could be applied also to the preconditioned problem BAu = Bf as we have done in Chapter 9 for the Galerkin method. No new theoretical questions arise here and therefore we have omitted these considerations.
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© 2002 Springer-Verlag Berlin Heidelberg
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Saranen, J., Vainikko, G. (2002). Trigonometric Collocation. In: Periodic Integral and Pseudodifferential Equations with Numerical Approximation. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04796-5_10
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DOI: https://doi.org/10.1007/978-3-662-04796-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07538-4
Online ISBN: 978-3-662-04796-5
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