On Rayleigh-Ritz and Collocation Methods for Solving Second Order Boundary Value Problems of Ordinary Differential Equations

Abstract

In this article, the Rayleigh-Ritz method is compared with the collocation method in solving second order boundary value problems of ordinary differential equations with the associated boundary conditions. The trial solution for the Rayleigh-Ritz method has to be chosen in such a way that the linearly independent functions must satisfy the boundary conditions. The collocation method, on the other hand make use of any basis function as the trial solution. The trial solution is then made to satisfy the differential equation and the boundary conditions at some interior points in the solution interval. Results obtained using the two methods show that the collocation method is simpler, easier and more accurate than the Rayleigh-Ritz method.