Third Derivative Block Method for the Direct Solution of Second-order Ordinary Differential Equations Using Two-step Hybrid Block Method of Order Ten

This research aim at developing two-step block third derivative method with two-offstep points for a direct solution of stiff second order ODEs. Power series approximation method was adopted as basis function using interpolation and collocation techniques at two selected grid points. We investigate some basic properties of our method and found it to converge. Stability region plotted shows that the method is A-stable and can handle stiff problems. The method was then tested on some highly stiff problems and numerical results presented side by side in tables’ shows that our method performs efficiently better on stiff and highly stiff problems as compared with an existing method.