IJPAM: Volume 105, No. 4 (2015)

NUMERICAL TREATMENT OF FREDHOLM INTEGRAL
EQUATIONS OVER $(0, +\infty)$ USING HILBERT TRANSFORM

F. Samadi$^1$, A. Omidi$^2$, R. Mohammad Hoseini$^3$
$^1$Department of Mathematics
Payame Noor University (PNU)
P.O. Box 19395-3697, Tehran, IRAN
$^2$Department of Applied Mathematics
Razi University
Kermanshah, IRAN
$^3$Department of Mathematics
Faculty of Science
Islamic Azad University
Central Tehran Branch
Tehran, IRAN


Abstract. In this paper, we present two types of integral equations of the second kind over semiaxis. Then we introduce a new numerical method by using the product rule, Nyström method and Hilbert Transform and prove that the proposed procedures are stable and convergent. The method reduces the integral equation to a system of linear algebraic equations. Some numerical examples are presented to show the efficiency and accuracy of the method.

Received: January 29, 2015

AMS Subject Classification: 45B05, 45G10

Key Words and Phrases: Fredholm integral equations, Nyström interpolation, Hilbert transform, Gaussian quadrature rules

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DOI: 10.12732/ijpam.v105i4.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 4
Pages: 549 - 560


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