Comparison Differential Transform Method with Homotopy Perturbation Method for Nonlinear Integral Equations

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Authors
Malihe Bagheri
 Department of mathematic,Golestan Institute of Higher Education,Gorgan,Iran.
Mahnaz Bagheri
 Departmen of mathematic, Islamic Azad University, behshahr branch, Iran.
Ebrahim Miralikatouli
 Department of mathematic,Golestan Institute of Higher Education,Gorgan,Iran.
Abstract
In this study, an application of differential transform method (DTM) is applied to solve the second kind of nonlinear integral equations such that Volterra and Fredholm integral equations. If the equation considered has a solution in terms of the series expansion of known function, this powerful method catches the exact solution. Comparison is made between the homotopy perturbation and differential transform method. The results reveal that the differential transform method is very effective and simple.
Keywords
 differential transform method
 Integral equation
 Volterra and Fredholm integral quations
MSC
References

[1]
J. Biazar, E. Babolian, R. Islam, Solution of a system of Volterra integral equations of the first kind by Adomian method, Appl. Math. Comput, 139 (2003), 249258.

[2]
K. Maleknejad, M. Tavassoli Kajani, solving linear integrodifferential equation system by Galerkin methods with hybrid functions, Appl. Math. Comput. , 159 (2004), 603612.

[3]
K. Maleknejad, F. Mirzaee, S. Abbasbandy, solving linear integrodifferential equations system by using rationalized Haar functions method, Appl. Math. Comput. , 155 (2004), 317328.

[4]
J. Biazar, H. Ghazvini, M. Eslami , He’s homotopy perturbation method for system of integral equations , Chaos solitons. Fractal, (2007), 06.001.

[5]
S. Q. Wang, J. H. He, Variational iteration method for solving integrodifferential equations, Phys. Lett.A., 367 (2007), 188191.

[6]
J. H. He, Homotopy technique and a perturbation technique for nonlinear problems, Int J. Non linear Mech., 35 (2000), 3743.

[7]
N. Bildik, A. Konuralp, Twodimensional differential transform method, Adomian’s decomposition method, and variational iteration method for partial differential equations, Int.J. Comput. Math., 83 (2006), 973987.

[8]
J. H. He, New interpretation of homotopy perturbation method, Internat. J. Modern Phys. B., 20 (2006), 25612568.

[9]
J. H. He, Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern Phys. B., 20 (2006), 11411199.

[10]
J. K. Zhou, Differential Transform and its Application for Electrical Circuits, Huazhong University Press, Wuhan, China (1968)

[11]
O. Ozdemir, M.O. Kaya, Flapwise bending vibration analysis of a rotating tapered cantilever BernoulliEuler bean by differential transform method , J. Sound Vid., 289 (2006), 413420.

[12]
A. Arikoglu, I. Ozkol , Solution of difference equations by using differential transform method, Appl. Math. Comput. , 174 (2006), 12161228.

[13]
A. Arikoglu, I. Ozkol, Solution of differentialdifference equations by using differential transform method, Appl. Math. Comput., 181 (2006), 153162.

[14]
A. Arikoglu, I. Ozkol , Solution of fractial differential equations by using differential transform method, Chaos Solitone. Fract. , 34 (2007), 14731481.

[15]
D. D. Ganji, G. A. Afrouzi, H. Hosseinzadeh, R. A. Talarposhti , Application of homotopyperturbation method to the second kind of nonlinear integral equations, Phys. Lett.A. , 371 (2007), 2025.

[16]
Z. Odibat, Differential Transform method for solving Volterra integral equations with separable kernels, Mathematics computational modeling, 48 (2008), 11441149.