Kristensen, Morten Rode2; Jørgensen, John Bagterp5; Thomsen, Per Grove6; Jørgensen, Sten Bay7
1 Computer Aided Process Engineering Center, Department of Chemical and Biochemical Engineering, Technical University of Denmark2 Department of Chemical and Biochemical Engineering, Technical University of Denmark3 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark4 Department of Informatics and Mathematical Modeling, Technical University of Denmark5 Copenhagen Center for Health Technology, Center, Technical University of Denmark6 Department of Applied Mathematics and Computer Science, Technical University of Denmark7 Centre for oil and gas – DTU, Center, Technical University of Denmark
A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge-Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the state integration, hereby minimizing the extra effort required for sensitivity integration. Through case studies the new algorithm is compared to an extrapolation method and to the more established BDF based approaches. Several advantages of the new approach are demonstrated, especially when frequent discontinuities are present, which renders the new algorithm particularly suitable for dynamic optimization purposes.
Computers and Chemical Engineering, 2004, Vol 28, Issue 12, p. 2695-2707