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Mathematical Problems in Engineering
Volume 2014, Article ID 147079, 7 pages
http://dx.doi.org/10.1155/2014/147079
Research Article

Polynomial Least Squares Method for the Solution of Nonlinear Volterra-Fredholm Integral Equations

Department of Mathematics, “Politehnica” University of Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania

Received 24 January 2014; Accepted 26 August 2014; Published 27 October 2014

Academic Editor: Gradimir Milovanović

Copyright © 2014 Bogdan Căruntu and Constantin Bota. 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. Y. Ordokhani, “Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized HAAr functions,” Applied Mathematics and Computation, vol. 180, no. 2, pp. 436–443, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Y. Ordokhani and M. Razzaghi, “Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized HAAr functions,” Applied Mathematics Letters, vol. 21, no. 1, pp. 4–9, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K. Maleknejad, S. Sohrabi, and Y. Rostami, “Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 123–128, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Yang, “Chebyshev polynomial solution of nonlinear integral equations,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 349, no. 3, pp. 947–956, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. Maleknejad, H. Almasieh, and M. Roodaki, “Triangular functions (TF) method for the solution of nonlinear Volterra-Fredholm integral equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3293–3298, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. Maleknejad and K. Nedaiasl, “Application of sinc-collocation method for solving a class of nonlinear Fredholm integral equations,” Computers & Mathematics with Applications, vol. 62, no. 8, pp. 3292–3303, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. H. R. Marzban, H. R. Tabrizidooz, and M. Razzaghi, “A composite collocation method for the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1186–1194, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. A. El-Ameen and M. El-Kady, “A new direct method for solving nonlinear Volterra-Fredholm-Hammerstein integral equations via optimal control problem,” Journal of Applied Mathematics, vol. 2012, Article ID 714973, 10 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. K. Parand and J. A. Rad, “Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5292–5309, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. H. Bhrawy, E. Tohidi, and F. Soleymani, “A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals,” Applied Mathematics and Computation, vol. 219, no. 2, pp. 482–497, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B. Ghanbari, “The convergence study of the homotopy analysis method for solving nonlinear Volterra-Fredholm integrodifferential equations,” The Scientific World Journal, vol. 2014, Article ID 465951, 7 pages, 2014. View at Publisher · View at Google Scholar