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Numerical solution of nonlinear Volterra-Fredholm integro-differential equations. (English) Zbl 1165.65404
Summary: The aim of this paper is to present an efficient analytical and numerical procedure for solving the high-order nonlinear Volterra-Fredholm integro-differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro-differential equation and the given conditions into the matrix equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
Full Text: DOI
[1] P. Darania, E. Abadian, A.V. Oskoi, Linearization method for solving nonlinear integral equations, Math. Probl. Eng. (2006) 1--10, Article ID 73714 · Zbl 1200.65109 · doi:10.1155/MPE/2006/73714
[2] Darania, P.; Abadian, E.: A method for the numerical solution of the integro-differential equations, Appl. math. And comput. 188, 657-668 (2007) · Zbl 1121.65127 · doi:10.1016/j.amc.2006.10.046
[3] P. Darania, M. Hadizadeh, On the RF-pair operations for the exact solution of some classes of nonlinear Volterra integral equations, Math. Probl. Eng. (2006) 1--11, Article ID 97020 · Zbl 1196.45003 · doi:10.1155/MPE/2006/97020
[4] Tang, T.; Mckee, S.; Diogo, T.: Product integration method for an integral equation with logarithmic singular kernel, Appl. numer. Math. 9, 259-266 (1992) · Zbl 0749.65099 · doi:10.1016/0168-9274(92)90020-E
[5] Diogo, A. T.; Mckee, S.; Tang, T.: A Hermite-type collocation method for the solution of an integral equation with a certain weakly singular kernel, IMA J. Numer. anal. 11, 595-605 (1991) · Zbl 0738.65096 · doi:10.1093/imanum/11.4.595
[6] Wazwaz, A. M.; El-Sayed, S. M.: A new modification of the Adomian decomposition method for linear and nonlinear operators, Appl. math. Comput. 122, 393-404 (2001) · Zbl 1027.35008 · doi:10.1016/S0096-3003(00)00060-6
[7] Kanwal, R. P.; Liu, K. C.: A Taylor expansion approach for solving integral equations, Int. J. Math. educ. Sci. technol. 3, 411-414 (1989) · Zbl 0683.45001 · doi:10.1080/0020739890200310
[8] Sezer, M.: Taylor polynomial solution of Volterra integral equations, Int. J. Math. educ. Sci. technol. 5, 625-633 (1994) · Zbl 0823.45005 · doi:10.1080/0020739940250501
[9] Kauthen, J. P.: Continuous time collocation method for Volterra--Fredholm integral equations, Numer. math. 56, 409 (1989) · Zbl 0662.65116 · doi:10.1007/BF01396646
[10] Yalcinbas, S.: Taylor polynomial solution of nonlinear Volterra--Fredholm integral equations, Appl. math. Comput. 127, 195-206 (2002) · Zbl 1025.45003 · doi:10.1016/S0096-3003(00)00165-X
[11] Yalcinbas, S.; Sezer, M.: The approximate solution of high-order linear Volterra--Fredholm integro-differential equations in terms of Taylor polynomials, Appl. math. Comput. 112, 291-308 (2000) · Zbl 1023.65147 · doi:10.1016/S0096-3003(99)00059-4
[12] Maleknejad, K.; Mahmoudi, Y.: Taylor polynomial solution of high-order nonlinear Volterra--Fredholm integro-differential equations, Appl. math. Comput. 145, 641-653 (2003) · Zbl 1032.65144 · doi:10.1016/S0096-3003(03)00152-8
[13] Darania, P.; Abadian, E.: Development of the Taylor expansion approach for nonlinear integro-differential equations, Int. J. Contemp. math. Sci. 1, No. 14, 651-664 (2006) · Zbl 1157.65516