Differential Algebraic Equations, Indices, and Integral Algebraic Equations.

摘要

In a recent report, Hairer defines the index of Differential Algebraic Equations (DAEs) by considering the effect of perturbations of the equations on the solutions. This index is called the perturbation index, pi. An earlier form of index used by a number of authors is determined by the number of differentiations of the DAEs that are required to generate an ordinary differential equation (ODE) satisfied by the solution. We will call this the differential index, di. Hairer gives an example whose differential index is one and perturbation index is two and other examples where they are identical. We will show that di less than or equal to pi less than or equal to di + 1 and that di = pi if the derivative components of the DAE are total differentials. This means that the differential components have a first integral. The integrals are a special case of a new type of integral equation we will call Integral Algebraic Equations (IAEs). 3 refs. (ERA citation 14:023901)