S. L. Lee and P. D. Hovland, "Sensitivity Analysis Using Parallel ODE Solvers and Automatic Differentiation inC: SensPVODE and ADIC," Preprint ANL/MCS-P818-0500, May 2000. [pdf]
PVODE is a high-performance ordinary differential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic differentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of AD-generated derivative code can reduce the time to solution over finite difference approximations.