SENSITIVITY ANALYSIS OF INITIAL-BOUNDARY-VALUE PROBLEMS WITH MIXED PDES AND ALGEBRAIC EQUATIONS - APPLICATIONS TO CHEMICAL AND BIOCHEMICAL SYSTEMS

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.