TY  - JOUR
T1  - An Accurate Continuous Hybrid Block Method for the Direct Solution of
General Second Initial Value Problem
AU - Abdelrahim, Ra`ft AU - Omar, Zurni AU - Hijazi, Mohamaad AU - Alsafi, Firas 
JO  - Journal of Modern Mathematics and Statistics
VL  - 13
IS  - 1
SP  - 15
EP  - 20
PY  - 2019
DA  - 2001/08/19
SN  - 1994-5388
DO  - jmmstat.2019.15.20
UR  - https://makhillpublications.co/view-article.php?doi=jmmstat.2019.15.20
KW  - Hybrid method
KW  -second order differential equation
KW  -power series
KW  -three off step points
KW  -block
KW  -IVPs
AB  - In this research, a new hybrid block method of order 5 for solving second order Initial Value Problems
(IVPs) is determined. One step with 3 off step points is used to generate the coefficients of the new method.
This method approximates the solutions of the second order IVPS at x<sub>n</sub>+1/6, x<sub>n</sub>+2/6, x<sub>n</sub>+3/6, x<sub>n+1</sub>, concurrently by using interpolation and collocation approach with fixed step size. The developed method don&#146;t need to reduce
the IVPs to its equivalent system of first order IVPs. The numerical results obtained show that the new method
outperforms the existing methods in terms of error.
ER  -