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Morten R. Kristensen, John B.
Jørgensen, Per G. Thomsen and Sten B. Jørgensen
An ESDIRK Method with
Sensitivity Analysis Capabilities
Computers and Chemical
Engineering, 28(12): 2695–2707, 2004
Abstract
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.
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