Three-Step Block Method for Solving Second Order Differential Equations

Abstract

In this paper, we developed a three-step block Method for numerical solution of second order differential equations using Legendre polynomials as the basic function. Interpolation and collocation procedures are used by choosing interpolation points at s=2 steps points using power series, while collocation points at r=k step points, using a combination of power series and perturbation term gotten from the Legendre polynomials, giving rise to a polynomial of degree r+s-2 and r+s equations. All the analysis on the scheme derived shows that it is stable, convergent and has region of Absolute Stability. Numerical examples were provided to test the performance of the method. Results obtained when compared with existing methods in the literature, shows that the method is accurate and efficient.