Abstract and Applied Analysis

An Iterative Scheme for Solving Systems of Nonlinear Fredholm Integrodifferential Equations

M. I. Berenguer, D. Gámez, and A. J. López Linares

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Abstract

Using fixed-point techniques and Faber-Schauder systems in adequate Banach spaces, we approximate the solution of a system of nonlinear Fredholm integrodifferential equations of the second kind.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 401541, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606196

Digital Object Identifier
doi:10.1155/2014/401541

Mathematical Reviews number (MathSciNet)
MR3232836

Zentralblatt MATH identifier
07022318

Citation

Berenguer, M. I.; Gámez, D.; López Linares, A. J. An Iterative Scheme for Solving Systems of Nonlinear Fredholm Integrodifferential Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 401541, 9 pages. doi:10.1155/2014/401541. https://projecteuclid.org/euclid.aaa/1412606196


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References

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Ş. Yüzbaş\i, 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • G. J. O. Jameson, Topology and Normed Spaces, Chapman & Hall, London, UK, 1974.
  • 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.
  • 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. \endinput