Partitions of the set of selected unknowns in linear differential–algebraic systems

Abstract

As was shown earlier, for a linear differential–algebraic system A₁y′ + A₀y = 0 with a selected part of unknowns (entries of a column vector y), it is possible to construct a differential system ỹ′ = Bỹ, where the column vector ỹ is formed by some entries of y, and a linear algebraic system by means of which the selected entries that are not contained in ỹ can be expressed in terms of the selected entries included in ỹ. In the paper, sizes of the differential and algebraic systems obtained are studied. Conditions are established under the fulfillment of which the size of the algebraic system is determined unambiguously and the size of the differential system is minimal.