Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 401541, 9 pages
http://dx.doi.org/10.1155/2014/401541
Research Article

An Iterative Scheme for Solving Systems of Nonlinear Fredholm Integrodifferential Equations

Departamento de Matemática Aplicada, E.T.S. Ingeniera Edificación, Universidad de Granada, C/Severo Ochoa s/n, 18071 Granada, Spain

Received 21 February 2014; Revised 28 May 2014; Accepted 6 June 2014; Published 6 July 2014

Academic Editor: Ahmet Yasar Ozban

Copyright © 2014 M. I. Berenguer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Danfu and S. Xufeng, “Numerical solution of integro-differential equations by using {CAS} wavelet operational matrix of integration,” Applied Mathematics and Computation, vol. 194, no. 2, pp. 460–466, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. A. Jafarian and S. Measoomy Nia, “Utilizing feed-back neural network approach for solving linear Fredholm integral equations system,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 5027–5038, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. K. Maleknejad, F. Mirzaee, and S. Abbasbandy, “Solving linear integro-differential equations system by using rationalized Haar functions method,” Applied Mathematics and Computation, vol. 155, no. 2, pp. 317–328, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. K. Maleknejad and M. Tavassoli Kajani, “Solving linear integro-differential equation system by Galerkin methods with hydrid functions,” Applied Mathematics and Computation, vol. 159, no. 3, pp. 603–612, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Pedas and E. Tamme, “A discrete collocation method for Fredholm integro-differential equations with weakly singular kernels,” Applied Numerical Mathematics, vol. 61, no. 6, pp. 738–751, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. J. Pour-Mahmoud, M. Y. Rahimi-Ardabili, and S. Shahmorad, “Numerical solution of the system of Fredholm integro-differential equations by the Tau method,” Applied Mathematics and Computation, vol. 168, no. 1, pp. 465–478, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Yalçinbaş, M. Sezer, and H. H. Sorkun, “Legendre polynomial solutions of high-order linear Fredholm integro-differential equations,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 334–349, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. E. Yusufoğlu, “Numerical solving initial value problem for Fredholm type linear integro-differential equation system,” Journal of the Franklin Institute, vol. 346, no. 6, pp. 636–649, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Ş. Yüzbaşı, N. Şahin, and M. Sezer, “Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases,” Computers & Mathematics with Applications, vol. 61, no. 10, pp. 3079–3096, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Zarebnia and M. G. Ali Abadi, “Numerical solution of system of nonlinear second-order integro-differential equations,” Computers & Mathematics with Applications, vol. 60, no. 3, pp. 591–601, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. I. Berenguer, M. A. Fortes, A. I. Garralda Guillem, and M. Ruiz Galán, “Linear Volterra integro-differential equation and Schauder bases,” Applied Mathematics and Computation, vol. 159, no. 2, pp. 495–507, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. R. Galán, and M. C. S. Pérez, “Analytical techniques for a numerical solution of the linear Volterra integral equation of the second kind,” Abstract and Applied Analysis, vol. 2009, Article ID 149367, 12 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, and M. C. Serrano Pérez, “Nonlinear Volterra integral equation of the second kind and biorthogonal systems,” Abstract and Applied Analysis, vol. 2010, Article ID 135216, 11 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. I. Berenguer, M. V. F. Muñoz, A. I. Garralda-Guillem, and M. R. Galán, “A sequential approach for solving the Fredholm integro-differential equation,” Applied Numerical Mathematics, vol. 62, no. 4, pp. 297–304, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. G. J. O. Jameson, Topology and Normed Spaces, Chapman & Hall, London, UK, 1974.
  16. B. R. Gelbaum and J. Gil de Lamadrid, “Bases of tensor products of Banach spaces,” Pacific Journal of Mathematics, vol. 11, pp. 1281–1286, 1961. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Semadeni, “Product Schauder bases and approximation with nodes in spaces of continuous functions,” Bulletin de l'Académie Polonaise des Sciences, vol. 11, pp. 387–391, 1963. View at Google Scholar · View at MathSciNet