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.


65R20 Numerical methods for integral equations
45D05 Volterra 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)
[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
[3] Akyüz-Dascloĝlu, A., 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
[5] Liu, H.M., Variational approach to nonlinear electrochemical system, Chaos, solitons fractals, 23, 2, 573-576, (2005)
[6] He, J.H., Homotopy perturbation technique, J. comput. meth. appl. mech. eng., 178, 34, 257-262, (1999) · Zbl 0956.70017
[7] Yusufogˇlu (Agadjanov), E., A homotopy perturbation algorithm to solve a system of fredholm – volterra type integral equations, Math. comput. model., (2007) · Zbl 1115.65131
[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), MR 16,179 · Zbl 0055.35803
[9] Delves, L.M.; Mohamed, J.L., Computational methods for integral equations, (1985), Cambridge University Press · 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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.