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Block by block method for the systems of nonlinear Volterra integral equations. (English) Zbl 1185.65237
Summary: The approach given in this paper leads to numerical methods for solving system of Volterra integral equations which avoid the need for special starting procedures. The method has also the advantages of simplicity of application and at least four order of convergence which is easy to achieve. Also, at each step we get four unknowns simultaneously. A convergence theorem is proved for the described method. Finally numerical examples presented to certify convergence and accuracy of the method.

65R20Integral equations (numerical methods)
45D05Volterra integral equations
Full Text: DOI
[1] Eltom, M. E.: Application of spline functions to system of Volterra integral equation of the first and second kinds, IMA, J. appl. Math. 17, 295-310 (1976) · Zbl 0323.45009 · doi:10.1093/imamat/17.3.295
[2] Maleknejad, K.; Shahrezaee, M.: Using Runge -- Kutta method for numerical solution of the system of Volterra integral equation, Appl. math. Comput. 149, 399-410 (2004) · Zbl 1038.65148 · doi:10.1016/S0096-3003(03)00148-6
[3] Akyüz-Dasclo&gcirc, A.; Lu: Chebyshev polynomial solutions of systems of linear integral equations, Appl. math. Comput. 151, 221-232 (2004) · Zbl 1049.65149
[4] Rabbani, M.; Maleknejad, K.; Aghazadeh, N.: Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method, Appl. math. Comput. 187, 1143-1146 (2007) · Zbl 1114.65371 · doi:10.1016/j.amc.2006.09.012
[5] Liu, H. M.: Variational approach to nonlinear electrochemical system, Chaos, solitons fractals 23, No. 2, 573-576 (2005) · Zbl 1135.76597
[6] He, J. H.: Homotopy perturbation technique, J. comput. Meth. appl. Mech. eng. 178, No. 34, 257-262 (1999) · Zbl 0956.70017
[7] Yusufog&caron, E.; (Agadjanov), Lu: A homotopy perturbation algorithm to solve a system of Fredholm -- Volterra type integral equations, Math. comput. Model. (2007)
[8] Young, A.: The application of approximate product-integration to the numerical solution of integral equations, Proc. roy. Soc. lond. Ser. A 224, 561-573 (1954) · Zbl 0055.35803 · doi:10.1098/rspa.1954.0180
[9] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations, (1985) · Zbl 0592.65093
[10] J. Biazara, H. Ghazvini, He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind, J. Chaos, Solitions Fractals (2007).