A three-step method based on Simpson's 3/8 rule for solving system of nonlinear Volterra integral equations

Document Type: Research Articles


1 Department of Mathematics, Islamic Azad University, Khorasgan Branch, Isfahan, Iran.

2 Department of Mechanic, Shahr-e-Kord University, Shahr-e-Kord, Iran.


This paper proposes a three-step method for solving nonlinear Volterra integral
equations system. The proposed method convents the system to a (3 × 3)
nonlinear block system and then by solving this nonlinear system we nd
approximate solution of nonlinear Volterra integral equations system. To show
the advantages of our method some numerical examples are presented.

[1] S. Abbasbandy, Numerical solutions of the integral equations: Homotopy
perturbation method and Adomian's decomposition method, Appl. Math.
Comput. 173 (2006), 493{500.
[2] A. Akyuz-Dasclo^glu, Chebyshev polynomial solutions of systems of linear
integral equations,Appl. Math. Comput. 151 (2004), 221{232.
[3] J. Biazar, H. Ghazvini, He's homotopy perturbation method for solving
systems of Volterra integral equations of the second kind, J. Chaos,
Solitions Fractals, 39 , (2009) 770{777.
[4] L. M. Delves, J. L. Mohamed, Computational Methods for Integral
Equations, Cambridge University Press, 1985.
[5] M. E. Eltom, Application of spline functions to system of Volterra integral
equation of the rst and second kinds, IMA, J. Appl. Math. 17 (1976),
[6] J. H. He, Homotopy perturbation technique, J. Comput. Meth. Appl.
Mech. Eng. 178 (1999), 257{262.
[7] H. M. Liu, Variational approach to nonlinear electrochemical system,
Chaos, Solitons Fractals, 23, (2005), 573{576.
[8] K. Maleknejad, M. Shahrezaee, Using Runge-Kutta method for numerical
solution of the system of Volterra integral equation, Appl. Math. Comput.
149 (2004), 399{410.
[9] M. Rabbani, K. Maleknejad, N. Aghazadeh, Numerical computational
solution of the Volterra integral equations system of the second kind by
using an expansion method, Appl. Math. Comput. 187 (2007), 1143{1146.
[10] Rostam K. Saeed, Chinars. Ahmed, Approximate solution for the system
of Non-linear Volterra integral Equations of the second kind by using
block-by-block method, Aust. J. Basic Appl. Sci, 2 (2008), 114{124.

[11] A. Young, The application of approximate product-integration to the
numerical solution of integral equations,Proc. Roy. Soc. Lond. Ser. A 224
(1954), 561{573.
[12] E. Yusufo^glu, A homotopy perturbation algorithm to solve a system
of Fredholm-Volterra type integral equations,Math. Comput. Model. 47
(2008), 1099{1107.