Abstract
In this manuscript, the two novel numerical methods for stiff ODEs-the Almost Runge-Kutta (ARK) and Aluffi-Pentini (AP)-are applied to the solution of two large stiff ODE systems that model the Belousov-Zhabotinskii reaction and air pollution process. The efficiency and accuracy of the two methods are compared revealing advantages of the ARK method especially for multidimensional ODE systems. © 2007 Springer Science+Business Media, LLC.