On a new class of splitting type iterative methods

Abstract

This paper deals with the stability analysis of a new class of iterative methods for elliptic problems. These schemes are based on a general splitting method, which decomposes a multidimensional parabolic problem into a system of 1D implicit problems. The solution of the given linear system of equations is approximated by p-component vector of approximations. Each splitted operator is applied to only one specific component of this vector. We use energy and spectral stability analysis and investigate the convergence rate of two iterative schemes. Finally, some results of numerical experiments are presented. The dependence of the convergence rate on the smoothness of the solution is investigated.