An algorithm for a numerical solution of differential-algebraic equations

Presented is the solution algorithm of the initial value problem (IVP) of the general implicit system of differential-algebraic equations (DAE) f(x,y,y')= 0. The system is linearized with respect to the polynomial coefficients in y and the solution is advanced by a single-step multi-stage collocation method. The algorithm turns out to be robust and stable, as well as a convenient tool for derivation of all possible collocation quadrature formulae and for designing their desired properties. The method is suitable for solving stiff differential equations and DAE's that arise in many mechanical, control and other systems.