About collocation-variational difference scheme for differential-algebraic equations

The article deals with the systems of ordinary differential equations with an identically degenerate matrix preceding a derivative (differential-algebraic equations). The initial condition is supposed to be consistent with the right-hand side, so the problem under consideration has a solution. We have given necessary definitions from the theory of solving differential-algebraic and stiff ordinary differential equations and shown the difficulties of their numerical solution. A special case of the collocation-variational method for solving differential-algebraic equations containing stiff components and having index not exceeding two. We have obtained the stability functions for the Dahlquist model equation, and made numerical calculations of the known test examples.