Numerical solution of Volterra nonlinear integral equations using modified parametric iteration method
Subject Areas : Electrical engineering (electronics, telecommunications, power, control)
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Keywords: Parametric iteration method, integral equations, numerical solution,
Abstract :
In this paper, we used the modified parametric iteration method to solve Volterra integral equations. The solution process is illustrated with several examples. A comparison between this method and the exact solution is made. The results show the simplicity and efficiency of the modified parametric iteration method. Also, the convergence of this method is investigated in this study. In this paper, we used the modified parametric iteration method to solve Volterra integral equations. The solution process is illustrated with several examples. A comparison between this method and the exact solution is made. The results show the simplicity and efficiency of the modified parametric iteration method. Also, the convergence of this method is investigated in this study. In this paper, we used the modified parametric iteration method to solve Volterra integral equations. The solution process is illustrated with several examples. A comparison between this method and the exact solution is made. The results show the simplicity and efficiency of the modified parametric iteration method. Also, the convergence of this method is investigated in this study. In this paper, we used the modified parametric iteration method to solve Volterra integral equations. The solution process is illustrated with several examples. A comparison between this method and the exact solution is made. The results show the simplicity and efficiency of the modified parametric iteration method.
[1] E. Coddington, N.Levinson. وTheory of Ordinary Differential Equations,
New York: McGraw-Hill, (1955).
[2] Sh.J. Liao, Beyond perturbation: Introduction to the Homotopy Analysis
Method, Boca Raton, Chapman & Hall/CRC Press (2003).
[3] J.H. He, Variational iteration method—a kind of non-linear analytical
technique: Some examples, International Journal of Nonlinear Mechanics 34
(4) (1999)699–708.
[4] J. Saberi-Nadjafi, M.Tamamgar The Variational iteration method: A highly
promising method for solving the system of integro-differential equations,
Computer & Mathematics with Application .56 (2008) 346-351.
[5]A.M. Wazwaz,The variational iteration method (VIM) for solving linear and
nonlinear Volterra integral and integro-differential equations, International
Journal of Computer Mathematics, 87(5) (2010) 1131-1141.
[6] M.Tamamgar , Kh.Maleknejad, An Approximate Method with High Accuracy for
Solving the Nonlinear Volterra Integral Equations,M.Tamamgar, Pacific Journal
of Applied Mathematics, Volume 8 Issue 3(2017)