Numerical Approach for Solving Stiff Differential Equations: A Comparative Study

Abstract

In this paper our attention is directed towards the discussion of phenomenon of stiffness and towards general purpose procedures for the solution of stiff differential equations. Our aim is to identify the problem area and the characteristics of the stiff differential equations for which the equations are distinguishable. Most realistic stiff systems do not have analytical solutions so that a numerical procedure must be used. Computer implementation of such algorithms is widely available e.g. DIFSUB, GEAR, EPISODE etc. The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDFs). In this study we focus on a particularly efficient algorithm which is named as EPISODE, based on variable coefficient backward differentiation formula. Through this study we find that though the method is very efficient it has certain problem area for a new user. All those problem area have been detected and recommended for further modification.