Numerical solution of weakly singular integro-differential equations

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DOI:

https://doi.org/10.26637/mjm302/008

Abstract

In this work, we prove the existence and uniqueness of the solution of weakly singular integro-differential equations. After some transformations direct numerical schemes using collocation methods are proposed for any peicewise closed contours.

Keywords:

Weakly singular integral equation, singular integral equation, approximation theory, collocation methods

Mathematics Subject Classification:

45D05, 45E05, 45L05, 45L10 , 65R20
  • Mostefa NADIR Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, 28000, Msila, Algeria.
  • Pages: 187-190
  • Date Published: 01-04-2015
  • Vol. 3 No. 02 (2015): Malaya Journal of Matematik (MJM)

A. Ayad, Spline approximation for first order Fredholm integro-differential equations, UniversitatisBabesBolyai. Studia. Mathematica 41 (1996), no. 3, 1-8.

L.M. Delves, J.L. Mohamed, Computational methods for integral equation, Cambridge University press, $(1985)$ DOI: https://doi.org/10.1017/CBO9780511569609

E. Ladopoulos, Singular Integral Equations: Linear and non- linear theory and its applications in science and engineering, 551p. Springer, Berlin, Heidelberg, New York (2000). DOI: https://doi.org/10.1007/978-3-662-04291-5_10

G. Micula and G. Fairweather, Direct numerical spline methods for first-order Fredholm integrodifferential equations, Revue d'Analyse Numerique et de Theorie de l'Approximation 22 (1993), no. 1,59-66.

M. NADIR, Adapted Quadratic Approximation for Logarithmic kernel Integrals, in Fasciculi mathematici 49, (2) pp 75-85 (2012)

M. NADIR, Numerical Solution of the Singular Integral Equations of the First Kind on the Curve, in Analele Universitatii de Vest,Timisoara Seria Matematica-Informatica 51 (1) pp 109-119 (2013). DOI: https://doi.org/10.2478/awutm-2013-0008

M. NADIR, Adapted linear Approximation for Logarithmic kernel Integrals, in Journal of Approximation Theory and Applied Mathematics 3 pp 37-44 ( 2014).

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Published

01-04-2015

How to Cite

Mostefa NADIR. “Numerical Solution of Weakly Singular Integro-Differential Equations”. Malaya Journal of Matematik, vol. 3, no. 02, Apr. 2015, pp. 187-90, doi:10.26637/mjm302/008.