A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method

Abdelaziz Mennouni; Nedjem Eddine Ramdani; Khaled Zennir

doi:10.5269/bspm.41734

Abdelaziz Mennouni University of Mostefa Ben Boulaid Batna 2
Nedjem Eddine Ramdani University of Mostefa Ben Boulaid Batna 2 https://orcid.org/0000-0003-1800-2154
Khaled Zennir Qassim University https://orcid.org/0000-0001-7889-6386

Resumo

In this paper, we present an ecient modication of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This -analytical method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.

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