求解隐式差分方程的一类高精度并行迭代法

为提高并行迭代法的计算精度,提出了一类高精度、无条件稳定、三层格式的并行迭代算法。用矩阵理论证明了迭代的收敛性,推证了网格加密时的渐进收敛性质。结果表明:对三层格式进行迭代处理,不仅能保证其计算精确度,而且具有很好的收敛速度与渐进收敛性质。数值算例验证了理论分析的正确性,表明了算法的可行性与有效性。

A Kind of Parallel Iterative Algorithm with High Accuracy for Solving Implicit Difference Equations

For improving the accuracy of algorithms, a kind of parallel iterative algorithm with high accuracy, unconditional stable and three-level scheme is studied in the paper. The property of convergence in iteration and the property of gradual-approach convergence are proved by matrix method. The theoretical analyses show that the high accuracy three-level implicit difference equations can be solved efficiently by iterative method in parallel. In addition, the good convergent rate and property of gradual-approach convergence are obtained. The numerical examples also show that the analyses are correct, and the algorithm is feasible and efficient.