On the numerical solution of multi-dimensional parabolic problem by the additive splitting up method Daoud S. Daoud Department of Mathematics, Eastern Mediterranean University, Via Mersin 10, Famagusta, North Cyprus, Turkey Abstract Several numerical methods arising from the difference methods for certain classes of two dimensional parabolic equation are based on an operator slitting. From the theo- retical 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. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Multi-dimensional parabolic equation; Splitting up method; Von Neumann stability 1. Introduction During the past five decades several time stepping methods have been introduced to approximate the two or three dimensional parabolic equations by the finite difference method that treats the space variables individually such E-mail address: daoud.daoud@emu.edu.tr (D.S. Daoud). 0096-3003/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2003.12.093 Applied Mathematics and Computation 162 (2005) 197–210 www.elsevier.com/locate/amc