Extended Hybrid Block Simpson's Method of the 5th and 6th Step-Sizes for Ordinary Differential Equations

We construct a self-starting Simpsons type block hybrid method (BHM) consisting of very closely accurate members each of order p=q+2 as a block. The higher order members of each were obtained by increasing the number k in the multi-step collocation (MC) used to derive the k-step continuous formula (5k6) through the aid of MAPLE software program. In this paper, we identify a continuous hybrid block schemes (CHBS) through the addition of one off-mesh collocation points in the MC. The (CHBS) is evaluated along with its first derivative where necessary to give a hybrid block schemes for a simultaneous application to the ordinary differential equations (ODEs}. The results of numerical experiment confirm the reliability of these schemes.