eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2015-10-30 3 6 220 225 10.12691/ajams-3-6-2 AJAMS2015362 article T. Aboiyar. 1 T. Luga. 1 B.V. Iyorter manversh@gmail.com 2 Department of Mathematics/Statistics/Computer Science, University of Agriculture, Makurdi, Nigeria Department of Mathematics and Computer Science, University of Mkar, Mkar, Nigeria This paper concerns the derivation of continuous linear multistep methods for solving first-order initial value problems (IVPs) of ordinary differential equations (ODEs) with step number k=3 using Hermite polynomials as basis functions. Adams-Bashforth, Adams-Moulton and optimal order methods are derived through collocation and interpolation technique. The derived methods are applied to solve two first order initial value problems of ordinary differential equations. The result obtained by the optimal order method compared favourably with those of the standard existing methods of Adams-Bashforth and Adams-Moulton. http://pubs.sciepub.com/ajams/3/6/2/ajams-3-6-2.pdf linear multistep method hermite polynomial collocation interpolation optimal order scheme ordinary differential equation initial value problem