European Journal of Scientific Research ISSN 1450-216X Vol.77 No.4 (2012), pp.580-588 © EuroJournals Publishing, Inc. 2012 http://www.europeanjournalofscientificresearch.com Starting Hybrid Stomer-Cowell More Accurately by Hybrid Adams Method for the Solution of First Order Ordinary Differential Equations Adesanya, A. Olaide Department of Mathematics, Modibbo Adama University of Technology Yola Adamawa State E-mail: adewale.james@aun.edu.ng Tel: +2348077092831; +2348184554615 Odekunle, M. Remilekun Department of Mathematics, Modibbo Adama University of Technology Yola Adamawa State James, A. Adewale Mathematics Division, American University of Nigeria Yola, Adamawa State, Nigeira Abstract Hybrid Stomer Cowell method was developed using the method of interpolation of the appropriate solution and collocation of the differential system. The method is implemented in predictor-corrector method in which Adams Bash method is developed to provide a non-reducing order predictor. Basic properties of the method were investigated and were found to be consistent, zero stable and converges. The efficiency of the method was tested on first order problems and was found to compare favourably with the existing methods. Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Predictor, Corrector, Converges, Efficiency. AMS Subject Classification Codes: 65L05, 65L06, 65D30 Introduction This paper considers the numerical solution of first order initial value problem of the form: ( ) ( ) 0 0 , y x y y x, f y = = ′ (1) where f is a given real valued function which is continuous within the interval of integration. We assumed that f satisfied Lipstichz condition that guaranteed the existence and the uniqueness of the solution to (1). Many scholars have developed linear multistep method for the solution of (1). They developed methods varying from discrete linear multistep method to continuous linear multistep method. According to Awoyemi (1992), continuous linear multistep method has greater advantages over the discrete method in that they give better error estimation, provide a simplified for of coefficient for