Laguerre polynomial solution of high- order linear Fredholm integro-differential equations

In this paper, a Laguerre matrix method is developed to find an approximate solution of linear differential, integral and integro-differential equations with variable coefficients under mixed conditions in terms of Laguerre polynomials. For this purpose, Laguerre polynomials are used in the interval [0,b]. The proposed method converts these equations into matrix equations, which correspond to systems of linear algebraic equations with unknown Laguerre coefficients. The solution function is obtained easily by solving these matrix equations. The examples of these kinds of equations are solved by using this new method and the results are discussed and it is seen that the present method is accurate, efficient and applicable.