Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Adjoint implementation of Rosenbrock methods applied to variational data assimilation problems
Journal of Computational Physics
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Forward, tangent linear, and adjoint runge-kutta methods in KPP–2.2
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
On the properties of runge-kutta discrete adjoints
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
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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.