Özyurt, Derya B.; Barton, Paul I. Cheap second order directional derivatives of stiff ODE embedded functionals. (English) Zbl 1076.65067 SIAM J. Sci. Comput. 26, No. 5, 1725-1743 (2005). Summary: A second order adjoint method is described for calculating directional derivatives of stiff ordinary differential equation (ODE) embedded functionals. The derivation of the general directional second order adjoint equations for point- and integral-form functionals is presented. A numerical procedure for calculating these directional derivatives that is relatively insensitive to the number of parameters is described and showcased. By combining automatic differentiation to obtain the adjoint and sensitivity equations with the staggered corrector method to solve the sensitivity systems, we achieve computational costs noticeably lower than directional finite differences based on a first order adjoint code. Cited in 7 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65L12 Finite difference and finite volume methods for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:second order adjoint method; Hessian-vector products; staggered corrector method; BDF method; van der Pol oscillator; heat equation; numerical examples; automatic differentiation; directional finite differences Software:TAMC; CVODES; DASPK 3.0; DASPKADJOINT PDFBibTeX XMLCite \textit{D. B. Özyurt} and \textit{P. I. Barton}, SIAM J. Sci. Comput. 26, No. 5, 1725--1743 (2005; Zbl 1076.65067) Full Text: DOI