解色散方程的AGE迭代方法

Alternating group explicit iteration for dispersive equation

为了设计求解色散方程Ut=auxxx的适合于并行机的差分数值方法,构造出求解色散方程的无条件稳定的三层隐式差分格式;该格式的局部截断误差为O(ι2+h2+ι2/h3)(其中ι和h分别为时间步长和空间步长).以此隐格式为基础,设计出交替分组显式(AGE)迭代方法,并证明了该迭代过程的收敛性.由于本方法的整个计算过程是显式的,非常适合于并行计算.数值算例表明,本方法具有良好的实用性.

In order to propose difference method that is suitable to parallel computer for solving dispersive e-quation u1= auxxx a three - level implicit difference scheme with unconditional is designed, its local truncation error is O(ι+ h2 + ι2/h ) , where T is time step size and h is space step size . Then on the base of this scheme, an alternating group explicit iteration ( AGEI) method is proposed and its convergence is proved. The AGE1 method is suitable for parallel arithmetic because it is an explicit method. A numerical example shows that the method has good applicability.