Abstract 

In this paper a modified Kutta’s Algorithm is derived through a tactful application of a geometric progression and binomialexpansion for rational powers. 

The new method is constructed from the traditional  Kutta’s formula, a one-step explicit method for the solution of initial value problems (IVPs) in ordinary 

differential equations.(ODEs) The performance of the new formula is test by numerical computation of some 

selected IVPs and the results compares favourably  with those from three other existing Runge-Kutta Methods It has also been proved that the method is absolutely stable, convergence, consistence anda very fast computing time. 

Keywords:modified Kutta algorithm, Initial value problem, ordinary Differential Equations and stability. 2010 Mathematical Subject Classification: Primary 65L20; Secondary 65L06