Robertson's Example For Stiff Differential Equations

. Robertson's example models a representative reaction kinetics as a set of three ordinary differential equations. After an introduction to the application in chemical engineering, a theoretical stiffness analysis is presented. Its results are confirmed by numerical experiments, and the performances of a non-stiff and a stiff numerical solver are contrasted. The methods used in this note showcase a possible approach to a problem, which is suspected to be stiff. Key words. Ordinary differential equations, stiffness, numerical methods, VODE, chemical engineering, reaction kinetics. AMS subject classifications. 65C20, 65L05, 80A30. 1 Introduction. In the original paper [5], Robertson states the problem as a system of ordinary differential equations x 1 = \Gamma0:04 x 1 + 10 4 x 2 x 3 ; x 1 (0) = 1; x 2 = 0:04 x 1 \Gamma 3 \Delta 10 7 x 2 2 \Gamma 10 4 x 2 x 3 ; x 2 (0) = 0; x 3 = 3 \Delta 10 7 x 2 2 ; x 3 (0) = 0: (1) The solutions x(t) = (x 1 (t); x 2 (t); x 3 (t)) T is..