Research On Parallel Algorithm For Two-dimensional Burgers Equations And Dispersive Equation With Diffusion

In this paper, the finite difference method for the initial-boundary problem of the Burgers equations in two space dimensions is considered. The equations are decomposed into two one-dimensional equations by the fractional step methods, and the numerical solution from nth time level to ( n + 1)th time level is computed by two steps. Firstly, two asymmetric difference schemes are proposed, and an alternating group explicit method (AGE) is constructed by using the two schemes at two adjacent points. We proved that the method is absolutely stable by linearization analysis methods. On the basis of the (AGE) method, an alternating segment implicit method is constructed, which each segment has 2p or p ( p≥3) points, and we prove the stability by linearization methods. With the fractional step methods, a great deal of numerical experiments and their results demonstrate that our methods have advantages of calculation briefness, higher precision and suitable for parallel computing.In the paper, we consider also an initial-periodic boundary condition of dispersive equation with diffusion. A new difference scheme and eight asymmetric schemes are proposed, and an alternating segment difference scheme is constructed. The scheme is absolutely stable and suitable for parallel computing. Numerical results demonstrate that the scheme has higher precision and good applicability.