A 2-Step Four-Point Hybrid Linear Multistep Method for Solving Second Order Ordinary Differential Equations Using Taylor’s Series Approach

This paper considers the development of a 2-step four-point continuous hybrid method for the direct solution of initial value problem (IVPs) of second order ordinary differential equations using the method of interpolation of the power series approximate solution and collocation of the differential system to develop our scheme. Taylor’s series approximation is used to analyze and implement yn+i i = 1...n-1 at xn+1, j = 0(1)2. The method is found to be consistent and zero-stable. Numerical results show a superior accuracy compared to existing methods.