Variational Iteration Method for Fredholm integral equations of the second kind
الموضوعات :
1 - Department of Mathematics, Faculty of Science, University of Guilan
2 - Department of Mathematics, Islamic Azad University, Rasht branch
الکلمات المفتاحية: Variational Iteration Method, FREDHOLM INTEGRAL EQUATION, Lagrange multiplier, RESTRICTED VARIATION,
ملخص المقالة :
In this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.
[1] He, J. H., Variational iteration method a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics, 34(4), 699-708, 1999.
[2] He, J. H., Variational iteration method-Some recent results and new interpretations, Journal of Computational and Applied Mathematics, 207, 3-17, 2007.
[3] Abbasbandy, S., Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method, Applied Mathematics and Computation, 173, 493-500, 2006.
[4] Golbabai, A., and Keramati, B., Modified homotopy perturbation method for solving Fredholm integral equations, Chaos, Solitons and Fractals, 2006 in press.
[5] Javidi, M., and Golbabai, A., Modified homotopy perturbation method for solving non-linear Fredholm integral equations, Chaos, Solitons and Fractals, 2007 in press.
[6] Ganji, D. D., Afrouzi, G. A., Hosseinzadeh, H., and Talarposhti, R. A., Application of homotopy-perturbation method to the second kind of the nonlinear integral equations, Physics Letters A, 371, 20-25, 2007.
[7] Taghizadeh, N., and Ebrahimi, H., The solution of Fredholm integral equations with degenerate kernel by Adomian decomposition method, Korean Annals of Math, 22, N0. 2, 163-172, 2005.
[8] Jerri, A. J., Introduction to integral equation with applications, 2th ed., John Wily and Sons, Inc., New York, 1999.
[9] Biazar, J., and Ghazvini, H., An analytical approximation to the solution of a wave equation by a Variational iteration method, Applied Mathematics Letters, 21 (8), 780-785, 2008.
[10] Biazar, J., and Ghazvini, H., He’s Variational iteration method for solving hyperbolic differential equations, International Journal of nonlinear sciences and numerical simulation 8 (3), 311-314, 2007.
[11] Biazar, J., and Ebrahimi, H., An Approximation to the Solution of Telegraph Equation by Variational Iteration Method, Numerical Methods for Partial Differential Equations, In press.
[12] Ganji, D. D., Nourollahi, M., and Mohseni, E., Application of He's methods to nonlinear chemistry problems, Computers and Mathematics with applications, 54 (7-8), 1122-1132, 2007.
[13] Dehghan, M., and Shakeri, F., Application of He’s Variation iteration method for solving the Cauchy reaction diffusion problem, Journal of computational and Applied Mathematics, 217 (2), 435-446, 2008.
[14] Abbasbandy, S., A new application of He's Variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials, Journal of Computational and Applied Mathematics, 207(1), 59-63, 2007.
