Abstract:

A high order parallel finite difference algorithm of a parabolic equation was presented. First,  the values of the previous three levels at the interface points were combined with the compact scheme to solve the values of subdomains in parallel, then the values at the interface points were computed by the compact scheme. The stability bound of the procedure was derived to be at least 23+16, and the convergence rate was proved to be of order four. Numerical examples show that this method has much better accuracy than  other  methods.

Key words: parabolic equation; parallel difference algorithm; fourthorder accuracy; domain decomposition methods