Numerical methods solving the semi-explicit differential-algebraic equations by implicit multistep fixed stepsize methods

We consider three classes of numerical methods for solving the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full, and modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and investigate their efficiency in theory and practice.