Document Type: Research Paper
Authors
- M. Matinfar ^{} ^{1}
- A. Riahifar ^{2}
^{1} Department of Mathematics, University of Mazandaran, Babolsar, PO. Code 47416-95447, Iran
^{2} Department of Mathematics, Islamic Azad University, Chalus Branch, PO. Code 46615-397, Iran
Abstract
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution of a system of linear algebraic equations with unknown generalized Laguerre coefficients. In addition, two examples are given to demonstrate the validity, efficiency and applicability of the technique.
Keywords
- Fredholm integro-differential equations
- unbounded domain
- generalized Laguerre polynomials
- Operational matrices
Main Subjects
[1] A. D. Polyanin, A. V. Manzhirov, Handbook of integral equations, Boca Raton, Fla., CRC Press, 1998.
[2] D. G. Sanikidze, On the numerical solution of a class of singular integral equations on an infinite interval, Differential Equations. 41(9) (2005), pp. 1353–1358.
[3] N. I. Muskhelishvili, Singular integral equations, Noordhoff, Holland, 1953.
[4] V. Volterra, Theory of functionnals of integro-differential equations, Dover, New York, 1959.
[5] F. M. Maalek Ghaini, F. Tavassoli Kajani, and M. Ghasemi, Solving boundary integral equation using Laguerre polynomials, World Applied Sciences Journal. 7(1) (2009), pp. 102–104.
[6] N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, and M. Hasan, Numerical solution of infinite boundary integral equation by using Galerkin method with Laguerre polynomials, World Academy of Science, Engineering and Technology. 47 (2008), pp. 334–337.
[7] D. Funaro, Approximations of Differential Equations, Springer-Verlag, 1992.
[8] J. Shen, T. Tang, and L. L. Wang, Spectral Methods Algorithms, Analysis and Applications, Springer, 2011.
[9] J. Shen, L. L. Wang, Some Recent Advances on Spectral Methods for Unbounded Domains, J. Commun. Comput. Phys. 5 (2009), pp. 195–241.