A 4-Point Block Method for Solving Second Order Initial Value Problems in Ordinary Differential Equations

摘要

This paper proposes a four-point block method for the numerical solution of second order ordinary differential equations. In the construction of the method, interpolation and collocation techniques were involved, while Legendre Polynomial served as both the interpolation and collocation equations. The proposed scheme was analyzed and it was found to be A-stable, consistent and convergent.Numerical examples of ordinary differential equations were solved using the proposed method to test its performance. The results obtained compared favourably with other methods considered.