### Approximate Solutions to Integral Equations by Wavelet Decomposition Methods

#### Abstract

We construct approximate solutions to Inverse Problems associated to equations of the form Af = g where A is an integral operator. For a given f , the Forward Problem consists in calculating its image through A, while the Inverse Problem looks for f for a given g. In order to solve the Inverse Problem we project the data into ﬁnite dimensional subspaces of wavelets in the context of a multiresolution analysis and solve the Foward Problem for each element of the basis by means of a Galerkin-type scheme. From these computations, we can accurately build a solution to the Inverse Problem based on properties of the chosen wavelets and suitable hyphotesis on the operator. We present examples related to fractional calculus.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**