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

Özet

In this paper, a collocation method based on Laguerre polynomials is presented to solve the systems oflinear differential equations. The Laguerre polynomials, their derivatives, the system of differential equations andthe conditions are written in the matrix form. Then, by using the constructed matrix forms, the collocation pointsand the matrix operations, the system of linear differential equations is transformed into a system of linear algebraicequations. The solution of this system gives the coefficients of the solutions forms. Thus, the solutions based onthe Laguerre polynomials is found. Also, an error estimation is presented by using residual functions.