| Abstract: | A finite difference domain decomposition algorithm (DDA) for solving the heat equation in parallel is presented. In this procedure, interface values between subdomains are calculated by the group explicit formula, whereas interior values of subdomains are determined by the classical implicit scheme. The stability and convergence for this DDA are proved. The stability bound of the procedure is derived to be eight times that of the classical explicit scheme. Though the truncation error at the interface is O(τ?+?h), L 2-error is proved to be O(τ?+?h 2). Numerical examples confirm the second-order convergence and indicate that the stability condition is sharp. A comparison of the numerical errors of this procedure with other known methods is also included. |
