On the numerical solution of multi-dimensional parabolic problem by the additive splitting up method

Several numerical methods arising from the difference methods for certain classes of two dimensional parabolic equation are based on an operator slitting. From the theoretical point of view the success and the evaluation of the splitting approach is primarily determined by the accuracy and the stability constrained. Most of the splitting methods defined in the past decades were of multiplicative non-parallel types with respect to the spatial variables. In 1994 Lui, Tai and Neittaanmaki presented a parallelisable implicit-splitting type of methods of different order of approximation and its of additive type with regard to the solution at the advanced time step. In this paper the stability analysis will be presented for the implicit splitting methods by Lu et al. and also we presented a parallelisable explicit splitting algorithm. Several model problems are solved by the splitting up algorithms to enhance the theoretical results and the concluding remarks.