Stability and convergence of a parallel fractional step method forthe solution of linear parabolic problems

Abstract

We analyze a parallel fractional step method for the solution oflinear parabolic systems. It can be viewed as a parallelization ofthe well-known θ-scheme. We perform an analysisof the convergence and stability of the scheme and we also studythe optimal choice of the parameters. We present some numericalresults corresponding to the solution of the classical heatequation.