An unconditionally stable parallel difference scheme for nonhomogeneous heat equation

We use an unconditionally stable parallel difference scheme to solve nonhomogeneous heat equation.This scheme is based on domain decomposition concept and is using asymmetric Saul yev schemes for internal nodes of each sub-domain and alternating group explicit method for subdomains interfacial nodes. This new scheme has several advantages such as: good parallelism, unconditional stability, fully explicit nature and better accuracy than original Saul yev schemes. The details of implementation are briefly discussed. Numerical experiment on stability and accuracy and CPU time are also presented.