BibTeX
@ARTICLE{
         Alexe2009Faa,
       title = "Forward and adjoint sensitivity analysis with continuous explicit {R}unge-{K}utta
         schemes",
       journal = "Applied Mathematics and Computation",
       volume = "208",
       number = "2",
       pages = "328--346",
       year = "2009",
       issn = "0096-3003",
       doi = "DOI: 10.1016/j.amc.2008.11.035",
       url =
         "http://www.sciencedirect.com/science/article/B6TY8-4V2NK83-1/2/722c0c442bc7ea44a74b86ed17ba6137",
       author = "Mihai Alexe and Adrian Sandu",
       keywords = "Sensitivity analysis, Dense output, Runge-Kutta pairs, Tangent linear models,
         Adjoint models, Automatic differentiation",
       abstract = "We study the numerical solution of tangent linear, first and second order adjoint
         models with high-order explicit, continuous Runge-Kutta pairs. The approaches currently implemented
         in popular packages such as SUNDIALS or DASPKADJOINT are based on linear multistep methods. For
         adaptive time integration of nonlinear models, interpolation of the forward model solution is
         required during the adjoint model simulation. We propose to use the dense output mechanism built in
         the continuous Runge-Kutta schemes as a highly accurate and cost-efficient interpolation method in
         the inverse problem run. We implement our approach in a Fortran library called DENSERKS, which is
         found to compare well to other similar software on a number of test problems."
}