Stability results for fractional step discretizations of time dependent coefficient evolutionary problems

We consider a class of additive Runge-Kutta methods, which include most of the classical alternating direction or fractionary step methods, for discretizing the time variable in an evolutionary problem whose coefficients depend on time. Some stability results are proven for these methods which, together with suitable consistency properties, permit us to show the convergence of these discretizations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved