Problem for differential-algebraic equations with a significant loads

Abstract

In this article, the problem for a differential-algebraic equation with a significant loads is studied. Unlike previously studied problems for differential equations with a significant loads, in the considered equation, there is a matrix in the left part with a derivative that is not invertible. Therefore, the system of equations includes both differential and algebraic equations. To solve the problem, we propose a modification of the Dzhumabaev’s parametrization method. The considered problem is reduced to a parametric problem for the differential-algebraic equation with significant loads. We apply the Weierstrass canonical form to this problem. We obtain parametric initial value problem for a differential equations and an algebraic equations with a significant loads. The solvability conditions for the considered problem are established.