Numerical Solution of the Singular Integral Equations of the First Kind on the Curve

Mostefa Nadir

doi:10.2478/awutm-2013-0008

.blurhash-client-img { display: none !important; }

Numerical Solution of the Singular Integral Equations of the First Kind on the Curve

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 51 (2013): Issue 1 (June 2013)

By: Mostefa Nadir

Open Access

|Aug 2013

Abstract

In this work we present a numerical solution for sin- gular integral equations of the first kind on the oriented smooth contour with Cauchy type kernel. For this one we use an adapted quadratic approximation constructed by the author for this goal, based on the Simpson rule. Many examples are treated in order to prove the eficiency of this approximation.

References

[1] D. J. Antidze, On the approximate solution of singular integral equations, Seminar of Institute of Applied Mathematics, Tbilissi, 1975.
Search in Google Scholar
[2] N. I. Muskhelishvili, Singular integral equations, Nauka Moscow, 1968, English transl, of 1sted Noordho , 1953; reprint, 1972.
Search in Google Scholar
[3] M. Nadir and J. Antidze, On the numerical solution of singular integral equations using Sanikidze's approximation, Comp Math in Sc Tech., 10(1), (2004), 83-89.10.12921/cmst.2004.10.01.83-89
Search in Google Scholar
[4] Nadir. M. and B. Lakehali, An approximation for singular integrals of Cauchy types, Advance in Algebra and Analysis (AAA) (1),1, 2006.
Search in Google Scholar
[5] M. Nadir and B. Lakehali, On The Approximation of Singular Integrals FEN DERG_IS_I (E-DERG_I). 2007, 2(2), 236-240.
Search in Google Scholar
[6] M. Nadir, Adapted Quadratic Approximation for Singular Integrals, Journal of Math- ematical Inequalities 4, (3), (2010), 423-430.10.7153/jmi-04-39
Search in Google Scholar
[7] J. Sanikidze, On approximate calculation of singular line integral, Seminar of Institute of Applied Mathematics, Tbilissi, 1970.
Search in Google Scholar
[8] J. Sanikidze, Approximate solution of singular integral equations in the case of closed contours of integration, Seminar of Institute of Applied Mathematics, Tbilissi, 1971.
Search in Google Scholar