Communications in Mathematics and Applications Vol. 8, No. 2, pp. 119–125, 2017 ISSN 0975-8607 (online); 0976-5905 (print) Published by RGN Publications http://www.rgnpublications.com Special Issue on Numerical Analysis and Applications Editor: Prof. Dr. Abdalah Rababah Artiﬁcial Bee Colony Algorithm for Solving Initial Value Problems Research Article L. Djerou 1, *, N. Khelil 2 and S. Aichouche 2 1 Department of Computer Science, M.K. University, Biskra, Algeria 2 Department of Mathematics, M.K. University, Biskra, Algeria *Corresponding author: ldjerou@yahoo.fr Abstract. A novel numerical differential equation method is presented to solve approximately an initial-value problem (IVP). The IVP is formulated as an optimization problem and the artiﬁcial bee colony algorithm (ABC) is used in order to ﬁnd numerical solutions for this problem. Finally, we use an initial value problem example as illustration to testify the efﬁciency of the proposed method. The computational results showed that the proposed new method is quite promising, and the potential of the algorithm could be applied successfully in near future to other numerical method as well. Keywords. Initial-value problem; Optimization problem; Artiﬁcial bee colony algorithm MSC. 65L05; 68T20 Received: February 17, 2017 Revised: May 28, 2017 Accepted: June 3, 2017 Copyright © 2017 L. Djerou, N. Khelil and S. Aichouche. 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. 1. Introduction Let f = f ( x, y) be a real-valued function of two real variables deﬁned for a ≤ x ≤ b, where a and b are ﬁnite, and for all real values of y. The equations  y ′ = f ( x, y) y(a) = y 0 , (1.1)