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 H 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.