Shannon wavelets for the solution of integrodifferential equations. (English) Zbl 1191.65174

Cattani, Carlo

Math. Probl. Eng. 2010, Article ID 408418, 22 p. (2010).

Summary: Shannon wavelets are used to define a method for the solution of integrodifferential equations. This method is based on (1) the Galerking method, (2) the Shannon wavelet representation, (3) the decorrelation of the generalized Shannon sampling theorem, and (4) the definition of connection coefficients. The Shannon sampling theorem is considered in a more general approach suitable for analysing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of \(L_{2}(\mathbb R)\) functions. Shannon wavelets are \(C^{\infty }\)-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series (connection coefficients).

MSC:

65R20	Numerical methods for integral equations
45B05	Fredholm integral equations
65T60	Numerical methods for wavelets

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