Document Type : Research Paper


Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili,m, P.O.Box 56199-11367, Ardabil, Iran.


In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k \sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examples that exhibit the exponential convergence rate.


[1] A. Akyuz-Dacslcouglu and M. Sezer,  Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations, Journal of the Franklin Institute, 342 (2005) 688-701.
[2] A. Arikoglu and I. Ozkol, Solutions of integral and integro-differential equation systems by using differential transform method, Computers and Mathematics with Applications, 56 (2008) 2411-2417.
[3] N. Eggert, M. Jarratt, and J. Lund, Sinc function computations of the eigenvalues of Strum-Lioville problems, J. Comput. Phys., 69 (1987) 209-229.
[4] J. Lund and K. Bowers, Sinc Methods For Quadrature and Differential Equations, SIAM, Philadelphia, PA, 1992.
[5] J. Lund and C. Vogel, A Fully-Galerkin method for the solution of an inverse problem in a parabolic partial differential equation. numerical solution of an inverse, Inverse Problems, 6 (1990) 205-217.
[6] J. Lund  and B.V. Rilay, A Sinc-collocation method for the computation of the eigenvalues of the radial Schrodinger equation, IMA J. Numer. Anal., 4 (1984) 83-98.
[7] I. Patlashenko, D. Givoli, and P. Barbone, Time-stepping schemes for system of Volterra integro-differential equations, Comput. Methods Appl. Mech. Engrg., 190 (2001) 5691-5718.
[8] J. Rashidinia and M. Zarebnia, Convergence of approximate solution of system of Fredholm integral equations, J. Math. Anal. Appl. 333 (2007) 1216--1227.
[9] R. Smith and K. Bowers, A Sinc-Galerkin estimation of diffusivity in parabolic problems, Inverse Problems, 9 (1993) 113-135.
[10] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993.
[11] E. Yusufouglu, Numerical solving initial value problem for Fredholm type linear integro-differential equation system,
Journal of the Franklin Institute, 346 (2009) 636--649.
[12] E. Yusufouglu, An efficient algorithm for solving integro-differential equations system, Applied Mathematics and Computation, 192 (2007) 51-55.