A note on underdetermined differential-algebraic equations

In the article interconnected linear systems of ordinary differ- ential and algebraic equations written in vector-matrix form are considered. Such formulations are frequently encountered in important applied prob- lems in energy, kinetic chemistry, biology, multi-link system modeling, and other fields. In Russian and international literature, they are commonly referred to as differential-algebraic equations. It is assumed that the num- ber of equations in the system is smaller than the dimension of the desired vector function. Using results from the theory of underdetermined systems of linear algebraic equations, the concept of a normal solution is developed for a singled out of problems. For their numerical solution, a variant of collocation-variational difference schemes based on solving a special type of mathematical (quadratic) programming problem is proposed. The results of numerical calculations of several model examples are presented, which illustrate the effectiveness of this approach.