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Delta basis functions and their applications for solving two-dimensional linear fredholm integral equations | ||
| Journal of Hyperstructures | ||
| دوره 4، شماره 1، شهریور 2015، صفحه 69-83 اصل مقاله (108.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2015.2599 | ||
| نویسندگان | ||
| F. Mirzaee* 1؛ Seyede Fatemeh Hoseini2؛ Khadijeh Mahdavi Moghadam2 | ||
| 1Department of Mathematics, Faculty of Science, Malayer University, Malayer, 65719- 95863, Iran. | ||
| 2Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719- 95863, Malayer, Iran | ||
| چکیده | ||
| In this paper an expansion method, based on twodimensional delta functions (2D-DFs), is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. The main characteristic behind this method is that this method reduce such problems to a system of algebraic equations. Since this approach does not need integration, all calculations can be easily implemented. Finally, we estimate the error of the method, and present two numerical examples to demonstrate the accuracy of the method. | ||
| کلیدواژهها | ||
| Two-dimensional delta functions؛ Operational matrix؛ Linear Fredholm integral equation | ||
| مراجع | ||
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[1] A. Alipanah, S. Esmaeili, Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function, J. Comput. Appl. Math.,235 (18) (2011) 5342-5347. [2] K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge Uni. Press (1997). [3] E. Babolian, S. Bazm, P. Lima, Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions, Commun. Nonl. Sci. Numer.Simul., 16 (2011) 1164-1175. [4] E. Babolian, K. Maleknejad, M. Roodaki, H. Almasieh, Two-dimensional trian-gular functions and their applications to nonlinear 2D Volterra-Fredholm integral equations, Comput. Math. Appl., 60 (2010) 1711-1722. [5] M.M. El-Borai, M. A. Abdou, M. Basseem, An Analysis of two dimesional inte-gral equations of the seconed kined, Le Matematiche, 62 (2007) 15-39. [6] L.M. Delves, J. L. Mohamed, Computational methods for integral equations, Cambridge Uni. Press, Cambridge (1985). [7] G. Han, J. Wang, Extrapolation of Nystr¨om solution for two dimensional nonlin-ear Fredholm integral equations, J. Comput. Appl. Math., 134 (2001) 259-268. [8] R. Hanson, J. Phillips, Numerical solution of two-dimensional integral equations using linear elements, SIAM J. Numer. Anal., 15 (1978) 113-121. [9] C. Hsio, Hybrid function method for solving Fredholm and Volterra integral equa-tions of the second kind, J. Comput. Appl. Math., 230(1) (2009) 59-68. [10] A.J. Jerri, Introduction to Integral Equations with Applications, John Wiley and Sons, INC (1999). [11] R.P. Kanwal, Linear integral equations, Academic Press, London (1971). [12] R. Kress, Linear integral equations, Springer, Berlin (1999). [13] F. Liang, F.R. Lin, A fast numerical solution method for two dimensional Fredholm integral equations of the second kind based on piecewise polynomial inter-polation, Appl. Math. Comput., 216 (2010) 3073-3088. [14] K. Maleknejad, S. Sohrabi, B. Baranji, Application of 2D-BPFs to nonlinear integral equations, Commun. Nonlin. Sci. Numer. Simul., 15 (2010) 527-535. [15] F. Mirzaee, S. Piroozfar, Numerical solution of the linear two-dimensional Fred-holm integral equations of the second kind via two-dimensional triangular orthogonal functions, J. King Saud Uni. Sci., 22 (2010) 185-193. [16] T. Okayama, T. Matsuo, M. Sugihara, Sinc-collocation methods for weakly sin-gular Fredholm integral equations of the second kind, J. Comput. Math. Appl.,234 (2010) 1211-1227. [17] K. Orav-Puurand, A. Pedas, G. Vainikko, Nystr¨om type methods for Fredholm integral equations with weak singularities, J. Comput. Appl. Math., 234 (2010)2848-2858. [18] Y. Ordokhani, M. Razzaghi, Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized Haar functions, Appl. Math. Lett., 21 (2008) 4-9. [19] M. Roodaki, H. Almasieh, Delta basis functions and their applications to systems of integral equations, Comput. Math. Appl., 63 (2012) 100-109. [20] W.J. Xie, F.R. Lin, A fast numerical solution method for two dimensional Fred-holm integral equations of the second kind, Appl. Num. Math., 59 (2009) 1709-1719. [21] A. Yildirim, Homotopi perturbation method for the mixed Volterra-Fredholm in-tegral equations, chaos, Solot. Fract., 42 (2009) 2760-2764. [22] S.A. Yousefi, A. Lotfi, Mehdi Dehghan, He’s variational iteration method for solving nonlinear mixed Volterra- Fredholm integral equations, Comput. Math. Appl., 58 (2009) 2172-2176. | ||
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