## Numerical solution of linear Volterra integral equations system of the second kind.(English)Zbl 1148.65101

Summary: There are several numerical approaches for solving systems of linear Volterra integral equations of the second kind. We present a method for numerical solution of a system of linear Volterra integral equations based on the power series method, the major advantage of which is being derivative-free. Also, this method reproduces the analytical solution when the exact solution is a polynomial. The numerical results prove that the presented method is very effective and simple. The software used for the numerical calculations in this study was MATLAB$$^{\circledR}7.4$$.

### MSC:

 65R20 Numerical methods for integral equations 45F05 Systems of nonsingular linear integral equations

Matlab
Full Text:

### References:

 [1] Burton, T.A., Volterra integral and differential equations, (2005), Elsevier B.V. Netherlands · Zbl 1075.45001 [2] 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 [3] Yalsinbas, S., Taylor polynomial solutions of nonlinear volterra – fredholm integral equations, Appl. math. comput., 127, 195-206, (2002) [4] Delves, L.M.; Mohamed, J.L., Computational methods for integral equations, (1985), Cambridge University Press Cambridge · Zbl 0592.65093 [5] Maleknejad, K.; Kajani, M.T.; Mahmoudi, Y., Numerical solution of Fredholm and Volterra integral equation of the second kind by using Legendre wavelets, Kybernetes, 32, 9-10, 1530-1539, (2003) · Zbl 1059.65127 [6] Sezer, M., Taylor polynomial solution of Volterra integral equations, Int. J. math. edu. sci. technol., 25, 5, 625, (1994) · Zbl 0823.45005 [7] Brunner, H., Collocation method for Volterra integral and related functional equations, (2004), Cambridge University Press Cambridge · Zbl 1059.65122 [8] Maleknejad, K.; Sohrabi, S.; Rostami, Y., Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials, Appl. math. comput., 188, 123-128, (2007) · Zbl 1114.65370 [9] Ghasemi, M.; Tavassoli Kajani, M.; Bobolian, E., Numerical solutions of the nonlinear volterra – fredholm integral equations by using homotopy perturbation method, Appl. math. comput., 188, 446-449, (2007) · Zbl 1114.65367 [10] 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
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.