Numerical solution of linear differential-algebraic systems of partial differential equations

A linear differential-algebraic system of partial differential equations of an arbitrary index is examined. The index of a differential-algebraic system is determined by the maximum degree (over the corresponding domain) of the elementary divisors corresponding to the zero and infinite roots of the characteristic polynomial of the matrix pencil constructed from the coefficients of this system. An iterative algorithm for the numerical solution of a differential-algebraic system is proposed. It is based on a special splitting of the associated matrix pencil and an application of the method of successive approximations to the split system. The stability of this method is shown, and its efficiency is demonstrated through test examples.