New stable group explicit finite difference method for solution of diffusion equation

A new group explicit method for solution of diffusion equation is presented. This method is based on domain decomposition concept and using asymmetric Saul’yev schemes for internal nodes of each sub-domain and alternating group explicit method for sub-domain’s interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability, fully explicit nature and better accuracy than original Saul’yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.