The Optimal Homotopy Asymptotic Method with Application to Second Kind of Nonlinear Volterra Integral Equations

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H. Ullah, S. Mukhtar, M. Nawaz, M. Adnan, The Optimal Homotopy Asymptotic Method with Application to Second Kind of Nonlinear Volterra Integral Equations, Int. J. Anal. Appl., 18 (1) (2020), 85-98.

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H. Ullah, S. Mukhtar, M. Nawaz, M. Adnan

Abstract

In this paper, we solved some problems of nonlinear second kind of Volterra integral equations by Optimal Homotopy Asymptotic Method(OHAM). We compared the results obtained by OHAM with the exact solutions of the problems. We find that the results obtained by OHAM are effective, simple and explicit from others analytical methods. We also showed the fast convergence of OHAM and list some examples to show the effectiveness of this method. In graphical analysis, we can see the exactness, accuracy and convergence of the method.The OHAM has mechanized steps that can be easily achieved with the help of Mathematica. All computational work and graphs are obtained by Mathematica 9.

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