Adapted linear approximation for singular integral equations

Mostefa NADIR; Belkacem LAKEHALI

doi:10.26637/mjm204/017

Abstract

The aim of this work is to solve singular integral equations (S.I.E), of Cauchy type on a closed smooth curve. This method presented by the author is based on the adapted linear approximation of the singular integral of the dominant part, where we reduce a (S.I.E) to an algebraic linear system and we realize numerically this approach by examples.

Keywords:

singular integral, interpolation, linear approximation, Holder space, Holder condition

Mathematics Subject Classification:

45D05, 45E05, 65R20

Authors Imprint References Funding Related Articles Downloads

Mostefa NADIR Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, 28000, Msila, Algeria.
Belkacem LAKEHALI Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, 28000, Msila, Algeria.

Pages: 497-501
Date Published: 01-10-2014
Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

D. J. ANTIDZE, On the approximate solution of singular integral equations, Seminar of Institute of Applied Mathematics, 1975, Tbilissi.

N. I. MUSKHELISHVILI, Singular integral equations, "Nauka" Moscow, 1968, English transl, of 1sted Noordhoff, 1953; reprint,1972.

M. NADIR, J. ANTIDZE, On the numerical solution of singular integral equations using Sanikidze's approximation, Comp Meth in Sc Tech. 10(1), 83-89 (2004). DOI: https://doi.org/10.12921/cmst.2004.10.01.83-89

M. NADIR, B. LAKEHALI, On The Approximation of Singular Integrals FEN DERGİSİ (E-DERGİ). 2007, $2(2), 236-240$

M. NADIR, Adapted linear Approximation for Singular Integrals, in Mathematical Sciences 6 (36), 2012. DOI: https://doi.org/10.1186/2251-7456-6-36

J. SANIKIDZE, On approximate calculation of singular line integral, Seminar of Institute of Applied Mathematics, 1970, Tbilissi

J. SANIKIDZE, Approximate solution of singular integral equations in the case of closed contours of integration, Seminar of Institute of Applied Mathematics, 1971, Tbilissi.

J. SARANEN, The modified quadrature method for logarithmic-kernel integral equations on closed curves, J. Integral Equations Appl. 3(4) (1991) 575-600. DOI: https://doi.org/10.1216/jiea/1181075650