Sampling boundary conditions for second order differential-algebraic equations

The article considers systems of second-order linear ordinary differential equations with an identically degenerated square matrix preceding the second derivative (second order differential-algebraic equations). Such problem statements often arise in applications. We have noted the difficulties in qualitative study and development of numerical methods for solving the equations under consideration. It is assumed that boundary conditions are given and their number is less than the doubled dimension of the initial system. We have defined a class of second order differential-algebraic equations, and using the known results of projection theory proposed an algorithm for sampling the missing boundary conditions. The method developed is illustrated by a simple example. At the conclusion of the article we have paid attention to the further research of this algorithm.