2D parallel and stable group explicit finite difference method for solution of diffusion equation

Recently various versions of alternating group explicit or alternating group explicit-implicit methods were proposed for solution of diffusion equation. The main benefits of these methods are: good stability, accuracy and parallelizing. But these methods were developed for 1D case and stability and accuracy were investigated for 1D case too. In the present study we extend the new group explicit method [R. Tavakoli, P. Davami, New stable group explicit finite difference method for solution of diffusion equation, Appl. Math. Comput. 181 (2006) 1379-1386] to 2D with operator splitting method. The implementation of method is discussed in details. Our numerical experiment shows that such 2D extension is unconditionally stable and it is more accurate that traditional unconditional stable explicit method.