University of TabrizComputational Methods for Differential Equations2345-39829220210401A Laguerre approach for solving of the systems of linear differential equations and residual improvement5535761075410.22034/cmde.2020.34871.1591ENSuayipYuzbasiDepartment of Mathematics, Faculty of Science,
Akdeniz University, TR 07058 Antalya, Turkey.0000-0002-5838-7063GamzeYildirimDepartment of Mathematics, Faculty of Science,
Akdeniz University, TR 07058 Antalya, Turkey.Journal Article20190726In this study, a collocation method based on Laguerre polynomials is presented to numerically solve systems of linear differential equations with variable coefficients of high order. The method contains the following steps. Firstly, we write the Laguerre polynomials, their derivatives, and the solutions in matrix form. Secondly, the system of linear differential equations is reduced to a system of linear algebraic equations by means of matrix relations and collocation points. Then, the conditions in the problem are also written in the form of matrix of Laguerre polynomials. Hence, by using the obtained algebraic system and the matrix form of the conditions, a new system of linear algebraic equations is obtained. By solving the system of the obtained new algebraic equation, the coefficients of the approximate solution of the problem are determined. For the problem, the residual error estimation technique is offered and approximate solutions are improved. Finally, the presented method and error estimation technique are demonstrated with the help of numerical examples. The results of the proposed method are compared with the results of other methodshttps://cmde.tabrizu.ac.ir/article_10754_4483e85df27b4d22c0556be887767d7a.pdf