摘要
研究求解抛物型方程三层隐式差分方程组的嵌套迭代并行算法 ,给出了此算法的构造过程 ,推导论证了它的迭代收敛条件和收敛趋向。该算法具有O(Δt3+Δx6)精确度阶和绝对稳定性 ,并对任意网比r和任意阶子方程组 ,迭代过程都是收敛的 ,且迭代收敛速度在每段中随网格点数P增加而增加。为提高迭代收敛速度 ,节省机时 ,还讨论了一类多点嵌套迭代算法 ,也给出了稳定条件、迭代收敛条件和收敛趋向。以上分析表明嵌套迭代并行算法对三层格式也是适用的 ,并且使并行算法的构造更加灵活。数值例子表明本算法具有高精度、高迭代收敛速度。
This paper studies the EOI parallel algorithm for the solution of three level implicit difference equations for solving parabolic equation. The algorithm is set up and its convergent condition of iteration and convergence trend are discussed. The algorithm is unconditionally stable and has the truncation error order O(Δt 3+Δx 6) . The iteration method is convergent for any r and any order subsystems. Its convergence rate increases with the increasing of the net point number p in each segment. In order to improve the convergence rate and save the computation time, we also develop a class of multi point EOI parallel algorithm and discuss its stability condition, convergent condition of iteration and convergence trend. Analysis above shows that the EOI parallel algorithm is suitable for the three level scheme and it makes the construction of the parallel algorithm more flexible. Numerical examples show that this algorithm has the properties of high accuracy, high convergence rate and high stability.
出处
《贵州大学学报（自然科学版）》
2004年第1期22-29,共8页
Journal of Guizhou University:Natural Sciences
关键词
高精度
抛物型方程
并行算法
收敛速度
稳定性
high accuracy
parabolic equation
parallel algorithm
convergence rate
stability
