Adaptive second derivative multistep methods for solving stiff chemical problems

In this paper, we introduce one-parameter families of multistep numerical methods for solving stiff initial value problems of ordinary differential equations. These methods are adaptive versions of second derivative backward differentiation formulas and their extensions. The stability properties of the proposed schemes are better than those of the main methods which make them suitable for solving stiff problems. Numerical experiments on some problems arising from chemical reactions verify the theoretical results.