Stability results for linearly implicit fractional step discretizations of non-linear time dependent parabolic problems

Some stability results are analyzed for a variant of fractional step Runge–Kutta methods which is designed to integrate efficiently semi-linear multidimensional parabolic problems. These schemes are shown to be linearly implicit in combination with a suitable splitting of the space differential operator. We also give a proof for the convergence of such schemes, by combining the stability results of this paper with the corresponding properties of consistency.