A matrix method for system ofintegro-di erential equations by usinggeneralized Laguerre polynomials

The purpose of this research is to present a matrix method for solving system of linear Fredholm integro-di erential 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) alongwith initial conditions are transformed into the matrix equations, which cor- responds to a system of linear algebraic equations with the unknown gen-eralized laguerre cofficients. combining these matrix equations and then solving the system yields the generalized Laguerre coe cients of the solution function. In addition, several numerical examples are given to demonstratethe validity, e ciency and applicability of the technique.

Keywords:

Systems of linear Fredholm integro-di erential equations , Un-bounded domain , Generalized Laguerre polynomials , Operational matrix ofintegration