An Efficient Third Derivative Hybrid Block Method of Order Eleven for the Direct Solution of Second-Order Ordinary Differential Equation

This paper proposes an efficient third derivative hybrid block method of order eleven for solving second Order Ordinary Differential Equations directly. Method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method was used, which was evaluated at non-interpolating points to give a contnuous block method. The discrete block method was recovered when the continuous block method was evaluated at all step points. The basic properties of the method were investigated and were found to be zero-stable, consistent, and convergent. The efficiency of the method was tested on some stiff equations and was found to give better approximation than the existing method compared with our result.