ZHANG Baojiu,PIAO Guangri.The numerical solution of generalized KdV - RLW - Rosenau equations based on POD method[J].Journal of Yanbian University,2022,(01):13-18.
基于POD方法的广义KdV - RLW - Rosenau方程的数值解
- Title:
- The numerical solution of generalized KdV - RLW - Rosenau equations based on POD method
- 文章编号:
- 1004-4353(2022)01-0013-06
- 关键词:
- 特征正交分解; 广义KdV - RLW - Rosenau方程; 降维模型; 数值分析
- Keywords:
- proper orthogonal decomposition; generalized KdV - RLW - Rosenau equation; reduced - orderd modeling; numerical analysis
- 分类号:
- O241.82
- 文献标志码:
- A
- 摘要:
- 讨论了KdV - RLW - Rosenau方程降维模型的数值解问题.首先在介绍半离散B样条Galerkin近似的基础上,应用Crank - Nicolson方法研究了全离散的B样条Galerkin格式; 然后将适当的特征正交分解(POD)方法应用于广义KdV - RLW- Rosenau方程的Galerkin finite element(GFE)格式,使其简化为低维度和高精度的POD GFE格式; 最后利用数值实验证明了所得结果的正确性.
- Abstract:
- This paper discusses the numerical solution of KdV - RLW - Rosenau in a reduced - order modeling.Firstly, based on the introduction of semi discrete B - spline Galerkin approximation, the fully discrete B - spline Galerkin scheme is studied by using Crank Nicolson method; And then, a proper orthogonal decomposition(POD)method is applied to a Galerkin finite element(GFE)formulation for generalized KdV - RLW - Rosenau equation such that it is reduced into a POD GFE formulation with lower dimensions and enough high accuracy; Finally, numerical experiments show the correctness of the results.
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备注/Memo
收稿日期: 2021-11-22
基金项目: 吉林省科技计划发展项目(20180101215JC)
第一作者: 张宝玖(1997—),男,硕士研究生,研究方向为数值计算.
通信作者: 朴光日(1968—),男(朝鲜族),博士,教授,研究方向为数值计算.