Numerical solution of DAE systems using block BDF methods

In this paper, a class of block backward differentiation formulas (BBDF) methods are discussed. Any formula in this class, which is characterized as k-block, is of order k, one-step and L-stable for any positive number k. These methods are suitable for the numerical solution of differential-algebraic equation (DAE) systems. The existence and numerical stability of the BBDF methods are presented as well as some convergence results for DAE systems. A selection of numerical examples show that our methods are both reliable and robust.