Stability Analysis of Differential-Algebraic Equations in AUTO_DAE

A new computational package (AUTO_DAE) to study the stability of index-1 differential-algebraic equations (DAEs) is presented. The characterization of the characteristic values of these systems is also presented and a discussion on the stability theorems for ordinary differential equations is performed for the differential-algebraic case. AUTO_DAE is based on the open source continuation and bifurcation computational package AUTO (Doedel et al., 1997), thoroughly used to investigate the behavior of ODEs. Prior to steady-state non linear analysis, AUTO_DAE performs a structural characterization of the DAEs in order to recognize the algebraic equations presented in the model. The characteristic values of the DAE system are evaluated using a standard routine to solve the generalized characteristic value problem. Reliability and robustness of the new code are demonstrated through the analysis of non linear chemical engineering problems.