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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:
65R20Integral equations (numerical methods)
45F05Systems of nonsingular linear integral equations
Software:
Matlab
WorldCat.org
Full Text: DOI
References:
[1] Burton, T. A.: Volterra integral and differential equations. (2005) · 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) · Zbl 1025.45003
[4] Delves, L. M.; Mohamed, J. L.: Computational methods for integral equations. (1985) · 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, No. 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, No. 5, 625 (1994) · Zbl 0823.45005
[7] Brunner, H.: Collocation method for Volterra integral and related functional equations. (2004) · 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.; Kajani, M. Tavassoli; 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