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.
Acknowledgments
The authors would like to express their great thankfulness to the referees for the comments and constructive suggestions very much, which are valuable in improving the quality of the original paper.
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Yifen Ke
Yifen Ke received a PhD degree from Fujian Normal University in 2017 and spent two years as a Postdoctoral Researcher at University of Chinese Academy of Sciences from 2017 until 2019. She is currently an Associate Professor in the College of Mathematics and Informatics at Fujian Normal University. Her research focuses on the design, analysis, and implementation of numerical methods for solving large-scale linear and nonlinear problems.
Changfeng Ma
Changfeng Ma graduated from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2003. He received his PhD degree in Computational Mathematics from the Chinese Academy of Sciences. Presently, he is a professor at Fujian Normal University.