The multilevel iterative method consists of the iterative systems associated with different levels, the solution in coarse level is in essence used as the initial guess of the iterative system in refined level. Since the different iterative targets, one doesn’t guarantee that an excellent coarse level solution provides better starting point than a bad one for the refined level system. To decrease computational cost a natural idea is to control the iterative times in coarse levels. The objective of this paper is to propose a multilevel iterative method for nonlinear partial different equations. In which a controlling parameter that can be used to choose the iterative times is introduced based on multiresolution error analysis, and a strategy of selecting iterative times is also proposed. Finally, an example is illustrated to show the effectiveness of our method given here
Deng, Xiaoyan and Gao, Hong
"A Multilevel Control Iterative Method for Nonlinear Partial Different Equations,"
Applied Mathematics & Information Sciences: Vol. 07:
4, Article 32.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss4/32