Applied Mathematical Sciences, Vol. 8, 2014, no. 164, 8199 - 8207 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.410807 On Numerical Solutions of Systems of Ordinary Differential Equations by Numerical-Analytical Method A. A. Opanuga, S. O. Edeki * , H. I. Okagbue, G. O. Akinlabi Department of Mathematical Sciences Covenant University, Canaanland, Otta, Nigeria * Corresponding author A. S. Osheku Department of Mathematics University of Ibadan, Ibadan, Nigeria B. Ajayi Department of Mathematics & Statistics Federal Polytechnic, Ado Ekiti, Nigeria Copyright © 2014 A. A. Opanuga, S. O. Edeki, H. I. Okagbue, G. O. Akinlabi, A. S. Osheku and B. Ajayi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper considers the solutions of systems of ordinary differential equations via a numeric-analytical method referred to differential Transforms Method (DTM). For numerical interpretation, two illustrative examples are used. The results obtained show a strong agreement with their corresponding exact solutions. The method is therefore proven to be effective and reliable, and as such, can be applied to systems of ODEs involving higher orders.