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

Y. Skwame, Kumleng G., Donald J. Z., J. Sunday

Abstract: 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.

Keywords: Continuous hybrid block schemes CHBS, Multi-step collocation MC, ODEs

How to Cite?: Y. Skwame, Kumleng G., Donald J. Z., J. Sunday, "Extended Hybrid Block Simpson's Method of the 5th and 6th Step-Sizes for Ordinary Differential Equations", Volume 5 Issue 5, May 2016, International Journal of Science and Research (IJSR), Pages: 282-288, https://www.ijsr.net/getabstract.php?paperid=NOV162652, DOI: https://dx.doi.org/10.21275/NOV162652