Laguerre collocation method for solutions of systems of linear differential equations

In this thesis, a collocation method based on Laguerre polynomials is presented to numerically solve systems of linear differential equations with variable coefficients of high order. Firstly, the Laguerre polynomials and their derivatives are written in matrix form. Then, the system of linear differential equations is reduced to a system of linear algebraic equations by means of matrix relations and collocation points. The conditions in the problem are written in the form of a matrix of Laguerre polynomials. A new system of linear algebraic equation is obtained by using the obtained algebraic system and the matrix form of the conditions. By solving the system of the obtained new algebraic equation, the coefficients of the approximate solution of the differential equation system problem are determined. For the problem, the residual error estimation technique is offered and approximate solutions are improved. The presented method and error estimation technique are explained by numerical examples. The results of the proposed method are compared with the results of other methods.