FATODE: a library for forward, adjoint and tangent linear integration of stiff systems

The FATODE, which is extracted from the KPP numerical libraray, is a Fortran programming library for the integration of stiff ODE systems. It incorporates a set of generic linear solvers suitable for large sparse systems. And the set allows users to add their own implementation conveniently. FATODE contains three families of methods – fully implicit Runge-Kutta methods, SDIRK methods and Rosenbrock methods. For each family, forward, adjoint and tangent linear models are implemented, which enables FATODE for direct and adjoint sensitivity analysis. In this paper, we describe the implementation aspects of FATODE, code organization and usage aspects. Then we demonstrate a simple example of its application on a small chemical mechanism for both ODE integration and sensitivity analysis.