Strategies for solving index one DAE with non-negative constraints: Application to liquid-liquid extraction

Liquid-liquid extraction modeling leads to solve an index one DAE system. For the sake of robustness, it is desirable to account for non-negative constraints. Based on the DASSL architecture (a classical index one DAE solver) we propose and compare three different strategies to implement these bound constraints. Each of these strategies corresponds to a different Newton modification: clipping, damping, or interior point method. The comparisons are made on two test cases: the Robertson ODE problem, and an example from liquid-liquid extraction modeling.