Integration of chemical stiff ODEs using exponential propagation method

In this paper, we study the numerical long time integration of large stiff systems of differential equations arising from chemical reactions by exponential propagation methods. These methods, which typically converge faster, use matrix-vector products with the exponential or other related function of the Jacobian that can be effectively approximated by Krylov sabspace methods. We equip these methods to an automatic stepsize control technique and apply the method of order 4 for numerical integration of some famous stiff chemical problems such as Belousov-Zhabotinskii reaction, the Chapman atmosphere, Hydrogen chemistry, chemical Akzo-Nobel problem and air pollution problem.