Laguerre collocation method for solving higher order linear boundary value problems

Collocation methods are efficient approximate methods developed by utilizing suitable set of functions known as trial or basis functions. These methods are used for solving differential equations, integral equations and integro-differential equations, etc. In this study, the Laguerre polynomial of degree 10 is used as a basis function to propose a collocation method for solving higher order linear ordinary differential equations. Four examples on 4 t h , 6 t h , 8 t h and 10 t h order ordinary differential equations are selected to illustrate the effectiveness of the method. The numerical results show that the proposed collocation method is easy and straightforward to implement, nevertheless, it is very accurate.