Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776220160901A matrix method for system of integro-differential equations by using generalized Laguerre polynomialsیک روش ماتریسی برای سیستمی از معادلات انتگرال-دیفرانسیل با استفاده از چندجمله ایهای لاگر تعمیم یافته85982449110.22067/ijnao.v6i2.45227ENM. MatinfarDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.A. RiahifarDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Journal Article19700101The purpose of this research is to present a matrix method for solving system of linear Fredholm integro-differential equations(FIDEs) of the second kind on unbounded domain with degenerate kernels in terms of generalized Laguerre polynomials(GLPs). The method is based on the approximation of the truncated generalized Laguerre series. Then the system of (FIDEs) along with initial conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown generalized Laguerre coefficients. Combining these matrix equations and then olving the system yields the generalized Laguerre coefficients of the solution function. In addition, several numerical examples are given to demonstrate the validity, efficiency and applicability of the technique.https://ijnao.um.ac.ir/article_24491_3000d6e1f047f1c6749d7c4435309721.pdf