ABSTRACT

In this paper, we introduce a class of SOR-like iteration methods for solving the systems of the weakly nonlinear equation, which is by reformulating equivalently the weakly nonlinear equation as a two-by-two block nonlinear equation. Two types of the global convergence theorems are given under suitable choices of the involved splitting matrix and parameter. Numerical results for the three-dimensional nonlinear convection-diffusion equation and the linear complementarity problem show that the proposed iteration methods are feasible and efficient for solving the weakly nonlinear equations.

中文翻译：

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求解弱非线性系统的类 SOR 迭代方法

摘要

在本文中，我们介绍了一类求解弱非线性方程组的类 SOR 迭代方法，即将弱非线性方程等价地重构为二乘二块非线性方程。Two types of the global convergence theorems are given under suitable choices of the involved splitting matrix and parameter. 三维非线性对流扩散方程和线性互补问题的数值结果表明，所提出的迭代方法对于求解弱非线性方程是可行和有效的。