Applications of the collocation method for ordinary differential equations

Engineering problems and physical events in nature can be permanently modeled thanks to differential equations. Approximate solutions are sought for which analytical solutions of such equations are not possible. The theory of differential equations has a lot of solution technics. In this study, applications of the collocation method in some initial value problems are discussed. It is shown how the solutions can be obtained by giving information about the mathematical history of the collocation method as a numerical method. Galerkin and Collocation methods emerge depending on the structure of the trial function used in the method, which is referred to as the weighted residual method. In the collocation method, various solutions were obtained by taking the Delta Dirac Function as the weight function in the weight residual method.