**ABSTRACT**

A One-step Extended Block Hybrid Formulae (OEBHF) for solving Orbital problems is presented. The processes compute the solutions of Orbital Problems in a block by block fashion by some discrete schemes obtained from the associated continuous schemes and its first derivatives which are combined and implemented as a set of block formulae. The analysis of the method was examined, it was found to be zero stable, consistence, convergent and A-stable. The order, error constants and the region of absolute stability was also investigated, MATLAB package was used to plot the region of stability within which the method is stable. Numerical results revealed this method to be efficient and very accurate, and especially suitable for orbital problems.

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