解非线性抛物型方程的多层网格扰动迭代法

Disturbed Iteration with Multiple-Grid for Solving Nonlinear Parabolic P. D. E.

提出一种数值求解非线性抛物型方程初边值问题的多层网格扰动迭代法；该方法有效地结合了多层网格方法和扰动迭代方法，在固定的时间网格层上该方法有二阶敛速，渐近最优；整体计算量为Ｏ（ＭＮ＿ｔ），其中Ｍ是时间计算层数目，Ｎ＿ｔ是空间分划细网层节点变量个数；计算误差不传播，且解决了迭代初值的选择问题。

The Multiple-Grid Disturbed Iteration(MDI)for solving discrete systems of parabolicpartial differential equations is presented.The numerical features of the MDI algorithm areindicated by the relevant analysis. MDI is provided with the quadratic converging rate and,asymptotically,only one iterative step per hj level is required.The convergence is indepen-dent of parameter h,and the amount of computing work is only O(Nl) at a fixed k level.MDI requires only simple calculation with explicit formulation and the amount of global com-puting work is of the order of O(MNl).The computing error is not accumulative and propa-gational, being from k=1 to m time levels.The MDI algorithm is also asymptotically opti-mal.