On self-regulating properties of collocation variational method for linear differential-algebraic equations

The article deals with linear interrelated systems of algebraic and ordinary differential equations, which are commonly occurring in important applied problems of power engineering, kinetic chemistry, biology, and other areas. In the literature, they are usually called differential-algebraic equations. We have emphasized the difficulties arising in the numerical solution of such problems and their characteristic properties, in particular, illposedness. The article described in detail the construction of one particular case of the collocation variational approach, which have given a good account of solving various classes of differential-algebraic equations. This approach is based on solving a specific problem of mathematical programming. Using a test example, we have shown that this difference scheme can generate a regularization algorithm (the so-called self-regulation property) with a regularization parameter - a grid step.