A high-order parallel finite difference algorithm

To solve the heat equation on parallel computers, a high-order parallel finite difference algorithm is presented. In this procedure, dividing the space domain into several sub-domains, we calculate the interface values between sub-domains by the classical explicit scheme, then solve the interior values of sub-domains by the forth-order compact scheme in parallel. The stability bound of the procedure is derived to be 1+63 times that of the classical explicit scheme. And the convergence rate is proved to be of order three. Numerical examples show that this method has much better accuracy than other known methods.