Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 3 6 2015 10 30 Derivation of Continuous Linear Multistep Methods Using Hermite Polynomials as Basis Functions 220 225 EN T. Aboiyar. T. Luga. B.V. Iyorter Department of Mathematics and Computer Science, University of Mkar, Mkar, Nigeria AJAMS2015362 10.12691/ajams-3-6-2 2015 7 11 2015 9 12 2015 10 28 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.