M. Caracotsios et We. Stewart, SENSITIVITY ANALYSIS OF INITIAL-BOUNDARY-VALUE PROBLEMS WITH MIXED PDES AND ALGEBRAIC EQUATIONS - APPLICATIONS TO CHEMICAL AND BIOCHEMICAL SYSTEMS, Computers & chemical engineering, 19(9), 1995, pp. 1019-1030
A robust numerical method is presented for integration and parametric
sensitivity analysis of nonlinear initial-boundary-value problems in a
timelike dimension t and a space dimension x. Mixed systems of partia
l differential and algebraic equations can be treated. Parametric deri
vatives of the calculated states are obtained directly via the local J
acobian of the state equations. Initial and boundary conditions are ef
ficiently reconciled. The method is able to handle jump conditions ind
uced by changes of equation forms at given t-values, or at unknown t-v
alues dependent on the solution. Transition points of the latter kind
are computed via a Newton scheme coupled with the step selection strat
egy of the integrator. The method is implemented in a portable FORTRAN
package PDASAC, and is illustrated with two examples from chemical an
d biochemical engineering. The acronym PDASAC stands for Partial-Diffe
rential-Algebraic Sensitivity Analysis Code.