53 © 2017 Conscientia Beam. All Rights Reserved. LOBATTO-RUNGE-KUTTA COLLOCATION AND ADOMIAN DECOMPOSITION METHODS ON STIFF DIFFERENTIAL EQUATIONS E. U. Agom 1+ F. O. Ogunfiditimi 2 Edet Valentine Bassey 3 1,3 Department of Mathematics University of Calabar Calabar Nigeria 2 Department of Mathematics University of Abuja Abuja Nigeria (+ Corresponding author) ABSTRACT Article History Received: 20 June 2017 Revised: 13 November 2017 Accepted: 28 November 2017 Published: 18 December 2017 Keywords Stiff differential equations, Adomian decomposition method, Lobatto-Runge-Kutta collocation method. JEL Classification: 65L05, 65L06, 65L07, 65D20. In this paper, we show the parallel of Adomian Decomposition Method (ADM) and Lobatto-Runge-Kutta Collocation Method (LRKCM) on first order initial value stiff differential equations. The former method provided closed form solutions while the latter gave approximate solutions. We illustrated these findings in two numerical examples. ADM solutions were in series form while those of LRKCM gave sizeable absolute error. We further visualized our findings in respective plots to show the great potentials of ADM over LRKCM in providing analytical solutions to stiff differential equations. Contribution/Originality: This study contributes in showing the originality of ADM in obtaining exact solution to Stiff differential equations, while LRKCM provided approximate solution whose accuracy depended on step size. 1. INTRODUCTION The exact solution of a stiff differential equation is typically associated with an exponent that has a large magnitude. It include a term that decay exponentially to zero as the independent variable increases, but whose derivative is much greater in magnitude than the term itself. This class of differential equation, in application, arise from phenomena with widely differing time (independent variable) scales. It is very common as mathematical models in physical and biological sciences. They occur in many fields of engineering science particularly in studies of electrical circuits, vibrations, chemical reactions and so on. There are ubiquitous in weather predictions, astrochemical kinetics, control systems and electronics. In general, it application is wide in industrial areas. A differential equation ) y , t ( f y   (1) is stiff if the exact solution include a term that decays exponentially to zero as t increases. Suppose such a term is t e   , where λ is a large positive constant. The kth derivative of this term is t k e e   , and the character k e forces International Journal of Mathematical Research 2017 Vol. 6, No. 2, pp. 53-59 ISSN(e): 2306-2223 ISSN(p): 2311-7427 DOI: 10.18488/journal.24.2017.62.53.59 © 2017 Conscientia Beam. All Rights Reserved.