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

Journal: International Journal of Science and Research (IJSR) (Vol.5, No. 5)

Publication Date:

Authors : ; ; ; ;

Page : 282-288

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

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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.

Last modified: 2021-07-01 14:37:34