Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE ITERATED PROJECTION METHOD FOR INTEGRO-DIFFERENTIAL EQUATIONS WITH CAUCHY KERNEL

  • Mennouni, Abdelaziz (Department of Mathematics, University of Mohamed el Bachir el Ibrahimi Bordj BouArreridj)
  • Received : 2012.05.07
  • Accepted : 2013.02.15
  • Published : 2013.09.30
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Abstract

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

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References

  1. K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge university press, 1997.
  2. K.E. Atkinson, Han, Theoretical Numerical Analysis: A Functional Analysis Framework, 3rd edition Springer-Verlag, 2009.
  3. K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge university press, 1997.
  4. H. Brezis, Analyse Fonctionnelle ,Dunod, Paris, 1999.
  5. A. Mennouni, A projection method for solving Cauchy singular integro-differential equations, Applied Mathematics Letters 25, (2012) 986-989. https://doi.org/10.1016/j.aml.2011.11.012
  6. A. Mennouni, S. Guedjiba, A note on solving integro-differential equation with Cauchy Kernel, Mathematical and Computer Modelling, 52 (2010) 1634-1638. https://doi.org/10.1016/j.mcm.2010.06.028
  7. A. Mennouni, S. Guedjiba, A note on solving Cauchy integral equations of the first kind by iterations, Applied Mathematics and Computation, 217 (2011) 7442-7447. https://doi.org/10.1016/j.amc.2011.02.040
  8. G. M. Phillips, Interpolation and Approximation by Polynomials, Springer, 2003.
  9. I. H. Sloan, B. J. Burn, N. Datyner, A new approach to the numerical solution of integral equations, J. Computational Phys., 18 (1975), 92105.
  10. I.H. Sloan, V. Thomee, Superconvergence of the Galerkin iterates for integral equations of the second kind, J. Integral Equations, 9 (1985), 2-23.