Solving stiff DAE systems as "near" index problems

Abstract: "This paper extends a numerical algorithm for solving nonlinear index problems of Chung and Westerberg [Ind. Eng. Chem. Res., 29 (1990), pp. 1234-1239] to include stiff DAE systems. Stiff DAE systems are shown to be near index problems. Near high index problems cannot be solved by existing stiff ODE/DAE solvers, such as LSODI. A stiff problem should be classified by index. Solutions to these problems can be expressed and controlled in terms of polynomials in the small coefficients which are responsible for the near singularity at the solution point. With the numerical algorithm suggested in this paper, stiff DAE systems can be solved accurately and stably even with explicit integration methods."