آمار
| تعداد نشریات | 45 |
| تعداد شمارهها | 1,511 |
| تعداد مقالات | 18,445 |
| تعداد مشاهده مقاله | 60,073,790 |
| تعداد دریافت فایل اصل مقاله | 21,157,504 |
Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials | ||
| Computational Methods for Differential Equations | ||
| مقاله 1، دوره 5، شماره 2، تیر 2017، صفحه 88-102 اصل مقاله (143 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Farshid Mirzaee* | ||
| Faculty of Mathematical Sciences and Statistics, Malayer University, P. O. Box 65719-95863, Malayer, Iran | ||
| چکیده | ||
| In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations which can be solved by an appropriate numerical method such as Newton’s method. Also, we show that the proposed method is convergent. Some examples are provided to illustrate the applicability, efficiency and accuracy of the suggested scheme. Comparison of the proposed method with other previous methods shows that this method is very accurate. | ||
| کلیدواژهها | ||
| Fredholm-Volterra integral equation؛ Bell polynomials؛ Collocation method؛ Operational matrix؛ Error analysis | ||
| مراجع | ||
|
[1] E. Babolian and M. Mordad, A numerical method for solving system of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl., 62 (2011), 187-198. [2] E. T. Bell, Exponential polynomials, Ann. of Math., 35 (1934), 258-277. [3] A. Bernardini and P. E. Ricci, Bell polynomials and dierential equations of Freud-type polyno-mials, Math. Comput. Model., 36 (2002), 1115-1119. [4] H. Brunner, On the numerical solution of Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal., 27(4) (1990), 87-96. [5] C. A. Charalambides, Enumerative Combinatorics, Chapman and Hall/CRC, Boca Raton, 2002. [6] L. Comtet, Advanced Combinatorics: The art of nite and in nite expansions, D. Reidel publishing co., Dordrecht, 1974. [7] L. M. Delves and J. L. Mohamed, Computational methods for integral equations, Cambridge University Press, Cambridge, 1985. [8] A. Di Cave and P. E. Ricci, Suipolinomidi Bell edinumeridi Fibonacciedi Bernoulli [On Bell polynomials and Fibonacci and Bernoulli numbers], Le Matematiche., 35 (1980), 84-95. [9] M. Gasca and T. Sauer, On the history of multivariate polynomial interpolation, J Comput. Appl. Math., 122 (2000), 23-35. [10] M. Ghasemi, M. Tavassoli Kajani, and E. Babolian, Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput., 188 (2007), 446-449. [11] F. A. Hendi and A. M. Albugami, Numerical solution for Fredholm-Volterra integral equation of the second kind by using collocation and galerkin methods, J. King Saud Uni., 22 (2010),37-40. [12] M. G. Kendall and A. Stuart, The advanced theory of statistics, Grin, London, 1958. [13] A. Kurosh, Coyrs d' Algebre Superieure, Editions Mir, Moscow, 1971. [14] K. Maleknejad, H. Almasieh, and M. Roodaki, Triangular functions (TFs) method for the solution of nonlinear Volterra-Fredholm integral equations, Commun. Nonlin. Sci. Numer. Simula., 15 (2010), 3293-3298. [15] J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003. [16] F. Mirzaee and E. Hadadiyan, Numerical solution of Volterra-Fredholm integral equations via modi cation of hat functions, Appl. Math. Comput., 280 (2016), 110-123. [17] Y. Ordokhani and 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. [18] J. Riordan, An introduction to combinatorial analysis, Wiley publication in mathematical statistics, John Wiley sons, New Yorks, 1958. [19] W. Wang and T. Wang, General identities on Bell polynomials, Comput. Math. Appl., 58 (2009), 104-118. [20] S. Yalcinbas, Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 127 (2002), 195-206. [21] S. Yousefi and M. Razzaghi, Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations, Math. Comput. Simula., 70 (2005), 419-428. | ||
|
آمار تعداد مشاهده مقاله: 1,778 تعداد دریافت فایل اصل مقاله: 1,806 |
||