Authors : Ra`ft Abdelrahim and Mohammed Odeh
Abstract: 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.
Ra`ft Abdelrahim and Mohammed Odeh, 2019. An Efficient Two Step Hybrid Block Approach for Solving Third Order Initial Value Problems Directly. Research Journal of Applied Sciences, 14: 97-102.