A three-step method based on Simpson's 3/8 rule for solving system of nonlinear Volterra integral equations
الموضوعات :M. Tavassoli-Kajani 1 , L. Kargaran-Dehkordi 2 , Sh. Hadian-Jazi 3
1 - Department of Mathematics, Islamic Azad University, Khorasgan Branch,
Isfahan, Iran.
2 - Department of Mechanic, Shahr-e-Kord University, Shahr-e-Kord, Iran.
3 - Department of Mechanic, Shahr-e-Kord University, Shahr-e-Kord, Iran.
الکلمات المفتاحية: Block by block method, System of Volterra integral equations, Simpson's 3/8 rule,
ملخص المقالة :
This paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe 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),
295{310.
[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.
