Zur Konvergenz des Peaceman-Rachford-Verfahrens

Summary In this paper we prove some results concerning the convergence of the Peaceman-Rachford iterative method. The main result covers both the stationary and the instationary case. No use is made of the so called commutativity condition which often was used in the literature in the instationary case. In proving the results of this paper it is made use of the theory of regular splittings which was introduced by R.S. Varga. Finally it is demonstrated how the results can be applied to discrete versions of elliptic boundary value problems.