Laguerre Collocation Method for Solutions of Systems of First Order Linear Differential Equations

Authors : Şuayip Yüzbaşi, Gamze Yildirim

Pages : 222-241

View : 12 | Download : 9

Publication Date : 2018-12-29

Article Type : Other

Abstract :In this paper, a collocation method based on Laguerre polynomials is presented to solve systems of linear differential equations. The Laguerre polynomials, their derivatives, system of differential equations and conditions are written in the matrix form. Then, by using the constructed matrix forms, collocation points and matrix operations, the system of linear differential equations is transformed into a system of linear algebraic equations. The solution of this system gives the coefficients of the solutions forms. Thus, the solutions based on the Laguerre polynomials is found. Also, error estimation is made by using residual functions. Numerical examples are given to explain the method. The results are compared with results of other methods.   
Keywords : Laguerre collocation method, Laguerre polynomials, systems of linear differential equations, Collocation method