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Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method. (English) Zbl 1114.65371
Summary: An expansion method is used for treatment of second kind Volterra integral equations system. This method gives an analytic solution for the system. The method reduces the system of integral equations to a linear system of ordinary differential equations. After constructing boundary conditions, this system reduces to a system of equations that can be solved easily with any of the usual methods. Finally, for showing the efficiency of the method we use some numerical examples.

65R20Integral equations (numerical methods)
45F05Systems of nonsingular linear integral equations
Full Text: DOI
[1] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · Zbl 0592.65093
[2] Ren, Y.; Zhang, Bo; Qiao, Hong: A simple Taylor-series expansion method for a class of second kind integral equations. J. comp. Appl. math 110, 15-24 (1999) · Zbl 0936.65146
[3] Maleknejad, K.; Aghazadeh, N.: Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. Appl. math. Comput. 161, 915-922 (2005) · Zbl 1061.65145
[4] Maleknejad, K.; Aghazadeh, N.; Rabbani, M.: Numerical solution of second kind Fredholm integral equations system by using a Taylor-series expansion method. Appl. math. Comput. 175, 1229-1234 (2006) · Zbl 1093.65124