Solution of Integral Equations of Volterra Type Using The Adomian Decomposition Method (ADM)
Keywords:Volterra type, integral equation, exact solution, Adomian decomposition method
This paper presents an alternative semi-analytical method for the solution of the Volterra integral equations. The solution of the Volterra integral equations has been decomposed into an infinite series of components via the Adomian decomposition method (ADM). Furthermore, four illustrative examples were solved to measure the performance of ADM in terms of suitability, convergence, and accuracy. Moreover, the results obtained via ADM were compared with the exact solution. Hence, ADM is found to be a good tool for the solution of Volterra integral equations and also minimizes the volume of calculations.
G. Adomian, Analytical solution of Navier-Stokes flow of a viscous compressible fluid, Foundations of Physics Letters, 8(4), 1995.
G. Adomian, A review of the Adomian decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135, pp. 501-544, 1988.
G. Adomian, Convergent series solution of nonlinear equations, Journal of Computational and Applied Mathematics, 11, pp. 225-230, 1984
G. Adomian, Solving frontier problems of physics: The decomposition method, Kluwer Academic Publishers, Boston, 1994.
G. Adomian and R. Rach, Modified Adomian Polynomials, Mathematical and Computer Modelling, 24(11), pp. 34-46, 1996.
 A. Alpinah and M. Dehghan, Numerical solution of the nonlinear Fredholm integral equations by positive definite functions, Appl. Math. Comput., pp. 1754–1761, 2007.
A. M. Batiha and B. Batiha, Differential transformation method for a reliable treatment of the nonlinear biochemical reaction model, Advanced Studies in Biology, vol. 3, pp. 355–360, 2011.
 R. Estrada and R. Kanwal, Singular integral equations, Birkhauser, Berlin, 2000.
F. Guerrero, F. J. Santonja, and R. J. Villanueva, “Solving a model for the evolution of smoking habit in Spain with homotopy analysis method,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 549–558, 2013.
 M. Gülsu and M. Sezer, A Taylor polynomial approach for solving differential-difference equations, J. Comput. Appl. Math., 186 (2), pp. 349-364. 2006.
J.H. He, A generalized variational principle in micromorphic thermo elasticity, Mech. Res. Com., 32(1), pp. 93–98, 2005.
J.H. He, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20(10), pp. 1141–1199, 2006.
Y. Keskin and G. Oturanç, Reduced differential transform method for partial differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 6, pp. 741–749, 2009.
M. Sezer, A method for the approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol., 27 (6), pp. 821-834, 1996.
 A.M. Wazwaz, A first course in integral equations, World Scientific Publishing Co. Pte. Ltd., Second Edition, Singapore, 2015.
A.M. Wazwaz, The modified decomposition method for analytic treatment of nonlinear integral equations and systems of non-linear integral equations, International Journal of Computer Mathematics, 82(9), pp. 1107–1115, 2005.
A.M. Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations, Journal of Computational and Applied Mathematics, 207, pp. 18–23, 2007
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