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

Volume 5, Issue 4, pp 288 - 296 http://dx.doi.org/10.22436/jmcs.05.04.06

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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.

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Keywords

• differential transform method
• Integral equation
• Volterra and Fredholm integral quations

MSC

•  45G15

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), 249-258.


• [2] K. Maleknejad, M. Tavassoli Kajani, solving linear integro-differential equation system by Galerkin methods with hybrid functions, Appl. Math. Comput. , 159 (2004), 603-612.


• [3] K. Maleknejad, F. Mirzaee, S. Abbasbandy, solving linear integro-differential equations system by using rationalized Haar functions method, Appl. Math. Comput. , 155 (2004), 317-328.


• [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 integro-differential equations, Phys. Lett.A., 367 (2007), 188-191.


• [6] J. H. He, Homotopy technique and a perturbation technique for non-linear problems, Int J. Non linear Mech., 35 (2000), 37-43.


• [7] N. Bildik, A. Konuralp, Two-dimensional differential transform method, Adomian’s decomposition method, and variational iteration method for partial differential equations, Int.J. Comput. Math., 83 (2006), 973-987.


• [8] J. H. He, New interpretation of homotopy perturbation method, Internat. J. Modern Phys. B., 20 (2006), 2561-2568.


• [9] J. H. He, Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern Phys. B., 20 (2006), 1141-1199.


• [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 Bernoulli-Euler bean by differential transform method , J. Sound Vid., 289 (2006), 413-420.


• [12] A. Arikoglu, I. Ozkol , Solution of difference equations by using differential transform method, Appl. Math. Comput. , 174 (2006), 1216-1228.


• [13] A. Arikoglu, I. Ozkol, Solution of differential-difference equations by using differential transform method, Appl. Math. Comput., 181 (2006), 153-162.


• [14] A. Arikoglu, I. Ozkol , Solution of fractial differential equations by using differential transform method, Chaos Solitone. Fract. , 34 (2007), 1473-1481.


• [15] D. D. Ganji, G. A. Afrouzi, H. Hosseinzadeh, R. A. Talarposhti , Application of homotopy-perturbation method to the second kind of nonlinear integral equations, Phys. Lett.A. , 371 (2007), 20-25.


• [16] Z. Odibat, Differential Transform method for solving Volterra integral equations with separable kernels, Mathematics computational modeling, 48 (2008), 1144-1149.