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

Year 2018, Volume: 10, 222 - 241, 29.12.2018

Şuayip Yüzbaşı , Gamze Yıldırım

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

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