Domain decomposition schemes with high-order accuracy and unconditional stability

Parallel finite difference schemes with high-order accuracy and unconditional stability for solving parabolic equations are presented. The schemes are based on domain decomposition method, i.e., interface values between subdomains are computed by the explicit scheme; interior values are computed by the implicit scheme. The numerical stability and error are derived in the H1H1 norm in one dimensional case. Numerical results of both one and two dimensions examining the stability, accuracy, and parallelism of the procedure are also presented.