Numerical solution of functional integral equations by the variational iteration method

In the present article, we apply the variational iteration method to obtain the numerical solution of the functional integral equations. This method does not need to be dependent on linearization, weak nonlinearity assumptions or perturbation theory. Application of this method in finding the approximate solution of some examples confirms its validity. The results seem to show that the method is very effective and convenient for solving such equations.

[1]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[2]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[3]  Khosrow Maleknejad,et al.  Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials , 2007, Appl. Math. Comput..

[4]  Ji-Huan He,et al.  Variational principles for some nonlinear partial differential equations with variable coefficients , 2004 .

[5]  Shaher Momani,et al.  Variational iteration method for solving nonlinear boundary value problems , 2006, Appl. Math. Comput..

[6]  Salih Yalçınbaş,et al.  Approximate solutions of linear Volterra integral equation systems with variable coefficients , 2010 .

[7]  A. Wazwaz The variational iteration method for exact solutions of Laplace equation , 2007 .

[8]  Ji-Huan He Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[9]  Ji-Huan He A new approach to nonlinear partial differential equations , 1997 .

[10]  M. T. Rashed Numerical solution of functional differential, integral and integro-differential equations , 2004, Appl. Math. Comput..

[11]  Jafar Biazar,et al.  He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind , 2009 .

[12]  M. T. Rashed,et al.  Numerical solutions of functional integral equations , 2004, Appl. Math. Comput..