Finite Difference Parallel Algorithms for Parabolic Equation

This paper discusses linear parabolic initial boundary value problem of a couple of new finite difference methods: For the first algorithm, a high order implicit scheme for solving heat equations, based on which a class of alternating group explicit iterative method (AGEI). The convergence analysis is provided and the results of numerical experiment are presented, which AGEI method is convergent and suitable for parallel computation. For the second algorithm, we propose a new high-precision domain decomposition algorithm for the parabolic equation based on the theories proposed by C. N. Dawson and the others. The new algorithm uses the Du Fort-Frankel scheme at the interface point as well as fully implicit scheme at interior points for the parabolic equation. As a result, our new method improves stability-condition without degrading the precision. Finally, we show that our results validate the effectiveness of our method.