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Original Articles

The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method

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Pages 1347-1357 | Received 14 Jul 2014, Accepted 21 Mar 2015, Published online: 26 May 2015

References

  • P. Assari, H. Adibi, and M. Dehghan, A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method, Numer. Algor. 67 (2014), pp. 423–455. doi: 10.1007/s11075-013-9800-1
  • K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.
  • K.E. Atkinson and J. Flores, The discrete collocation method for nonlinear integral equations, IMA J. Numer. Anal. 13 (1993), pp. 195–213. doi: 10.1093/imanum/13.2.195
  • K. E. Atkinson and F.A. Potra, Projection and iterated projection methods for nonlinear integral equations, SIAM J. Numer. Anal. 24 (1987), pp. 1352–1373. doi: 10.1137/0724087
  • E. Babolian and A. Shahsavaran, Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets, J. Comput. Appl. Math. 225 (2009), pp. 87–95. doi: 10.1016/j.cam.2008.07.003
  • H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, 2004.
  • M. Dehghan and R. Salehi, The numerical solution of the non-linear integro-differential equations based on the meshless method, J. Comput. Appl. Math. 236 (2012), pp. 2367–2377. doi: 10.1016/j.cam.2011.11.022
  • H. Kaneko and Y. Xu, Degenerate kernel method for Hammerstein equations, Math. Comput. 56 (1991), pp. 141–148. doi: 10.1090/S0025-5718-1991-1052097-9
  • H. Kaneko, R. D. Noren, and B. Novaprateep, Wavelet applications to the Petrov–Galerkin method for Hammerstein equations, Appl. Numer. Math. 45 (2003), pp. 255–273. doi: 10.1016/S0168-9274(02)00173-3
  • M.A. Krasnosel'skii and P.P. Zabareiko, Geometric Methods of Nonlinear Analysis, Springer, Berlin, 1984.
  • S. Kumar and I. Sloan, A new collocation-type method for Hammerstein integral equations, Math. Comput. 48 (1987), pp. 585–593. doi: 10.1090/S0025-5718-1987-0878692-4
  • H. Laeli Dastjerdi and F.M. Maalek Ghaini, Numerical solution of Volterra–Fredholm integral equations by moving least square method and Chebyshev polynomials, Appl. Math. Mode. 36 (2012), pp. 3283–3288. doi: 10.1016/j.apm.2011.10.005
  • P. Lancaster and K. Salkauskas, Surfaces generated by moving least squares methods, Math. Comput. 37 (1981), pp. 141–158. doi: 10.1090/S0025-5718-1981-0616367-1
  • D. Mirzaei and M. Dehghan, A meshless based method for solution of integral equations, Appl. Numer. Math. 60 (2010), pp. 245–262. doi: 10.1016/j.apnum.2009.12.003
  • D. Mirzaei, R. Schaback, and M. Dehghan, On generalized moving least squares and diffuse derivatives, IMA J. Numer. Anal. 32 (2012), pp. 983–1000. doi: 10.1093/imanum/drr030
  • D. O'Regan, Existence results for nonlinear integral equations, J. Math. Anal. Appl. 192 (1995), pp. 705–726. doi: 10.1006/jmaa.1995.1199
  • R. Salehi and M. Dehghan, A generalized moving least square reproducing kernel method, J. Comput. Appl. Math. 249 (2013), pp. 120–132. doi: 10.1016/j.cam.2013.02.005
  • R. Salehi and M. Dehghan, A moving least square reproducing polynomial meshless method, Appl. Numer. Math. 69 (2013), pp. 34–58. doi: 10.1016/j.apnum.2013.03.001
  • D. Shepard, A Two-dimensional Interpolation Function for Irregularly Spaced Points, in Proceedings of the 23rd National Conference on ACM, ACM Press, New York, 1968, pp. 517–524.
  • F.G. Tricomi, Integral Equations, Dover, New York, 1982.
  • G. Vainikko, Perturbed Galerkin method and general theory of approximate methods for nonlinear equations, USSR Comput. Math. Math. Phys. 7 (1967), pp. 1–41. doi: 10.1016/0041-5553(67)90140-1
  • H. Wendland, Scattered Data Approximation, Cambridge University Press, Cambridge, 2005.
  • C. Zuppa, Error estimates for moving least square approximations, Bull. Braz. Math. Soc, New Series 34 (2001), pp. 231–249. doi: 10.1007/s00574-003-0010-7

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