Numerical solution of Fredholm integral-differential equations on unbounded domain
الموضوعات :
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
الکلمات المفتاحية: Fredholm integro-differential equations, unbounded domain, generalized Laguerre polynomials, Operational matrices,
ملخص المقالة :
In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution ofa system of linear algebraic equations with unknown generalized Laguerre coefficients. Inaddition, two examples are given to demonstrate the validity, efficiency and applicability ofthe technique.
[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.
