An index reduction method for solving differential algebraic equations

Abstract

Abstract For years, chemical engineering researchers were interested in higher index differential algebraic equations which may arise when modeling dynamic systems. With the index reduction methods, they have found ways for obtaining index-one systems which can be solved by means of numerical integrators. Unfortunately, the systems calculated by such methods may be much bigger than the initial ones, and furthermore they may be not strictly equivalent to them. We introduce an index reduction method which overcomes both drawbacks: each deflation step reduces the number of differential equations and generates as much algebraic equations. More precisely, those algebraic equations are constraints hidden in the differential equations obtained at the previous deflation step. The iterative deflation process stops when the differential equations involve only a minimal set of dynamic variables from which the other dynamic variables depend implicitly according to the algebraic constraints. Consequently, such a reduction method has not only a numerical interest but also helps in gaining a deeper insight into a dynamic model.