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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 278097, 6 pages
http://dx.doi.org/10.1155/2013/278097
Research Article

Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Gelugor, Penang, Malaysia

Received 20 April 2013; Accepted 16 June 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Mohammad Almousa and Ahmad Ismail. 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. A. Adawi, F. Awawdeh, and H. Jaradat, “A numerical method for solving linear integral equations,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 9–12, pp. 485–496, 2009. View at MathSciNet
  2. M. H. AliAbadi and S. Shahmorad, “A matrix formulation of the tau method for Fredholm and Volterra linear integro-differential equations,” The Korean Journal of Computational & Applied Mathematics, vol. 9, no. 2, pp. 497–507, 2002. View at MathSciNet
  3. S. Abbasbandy, “Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 493–500, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  4. F. Mirzaee, “Numerical solution for Volterra integral equations of the first kind via quadrature rule,” Applied Mathematical Sciences, vol. 6, no. 17–20, pp. 969–974, 2012. View at MathSciNet
  5. S. Abbasbandy and E. Babolian, “Automatic augmented Galerkin algorithms for linear first kind integral equations: non-singular and weak-singular kernels,” Bulletin of the Iranian Mathematical Society, vol. 21, no. 1, pp. 35–62, 1995. View at MathSciNet
  6. V. Marinca and N. Herişanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 35, no. 6, pp. 710–715, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Herişanu, V. Marinca, T. Dordea, and G. Madescu, “A new analytical approach to nonlinear vibration of an electrical machine,” Proceedings of the Romanian Academy. Series A, vol. 9, no. 3, pp. 229–236, 2008.
  8. M. S. Hashmi, N. Khan, and S. Iqbal, “Optimal homotopy asymptotic method for solving nonlinear Fredholm integral equations of second kind,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 10982–10989, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. Sulaiman and I. Hassan, “Successive approximation method (S.A.M.) for solving integral equation of the first kind with symmetric kernel,” Journal of Education and Sciences, vol. 21, no. 4, pp. 149–159, 2008.
  10. A. J. Mohammed and J. I. Mustafa, “Construction of a new technique in Aitken extrapolation method for solving Fredholm integral equation of the first kind with iterated kernel,” Journal of Education and Sciences, vol. 21, no. 2, pp. 143–149, 2008.