TY  - JOUR
T1  - An Efficient Two Step Hybrid Block Approach for Solving Third
Order Initial Value Problems Directly
AU - Abdelrahim, Ra`ft AU - Odeh, Mohammed 
JO  - Research Journal of Applied Sciences
VL  - 14
IS  - 4
SP  - 97
EP  - 102
PY  - 2019
DA  - 2001/08/19
SN  - 1815-932x
DO  - rjasci.2019.97.102
UR  - https://makhillpublications.co/view-article.php?doi=rjasci.2019.97.102
KW  - two off step points
KW  -power series
KW  -third order differential equation
KW  -block method
KW  -Hybrid method
KW  -numerical
AB  - Solving Ordinary value problems (ODEs) numerically is an area that has drawn much consideration
in latest literature and hence, the general object of this study. In this study, new hybrid block method is
proposed using collocation and interpolation approach and then is employed to approximate third order initial
value problems directly. Certain conditions of the block method established include it being of step
number k = 2 with two off-step points. This hybrid block method involves of mathematical expressions that will
concurrently supply results at the step and off-step points. Numerical properties which involve zero stability,
order of the method, consistency and convergence are established. After that some third order initial value
problems are considered and the new hybrid block method is employed to solve it numerically and comparison
was made with existing methods in terms of error. The generated numerical results show superiority of the new
method in terms of error. Therefore, this developed hybrid block method can be adopted a more appropriate
numerical approach to approximate the third order IVPs numerically.
ER  -