解算器
趋同(经济学)
反应扩散系统
数值分析
数学
应用数学
偏微分方程
计算机科学
班级(哲学)
数学优化
数学分析
人工智能
经济增长
经济
作者
Shuang Liu,Yihong Du,Xinfeng Liu
标识
DOI:10.1080/00207160.2019.1599868
摘要
It is always very difficult to efficiently and accurately solve a system of differential equations coupled with moving free boundaries, while such a system has been widely applied to describe many physical/biological phenomena such as the dynamics of spreading population. The main purpose of this paper is to introduce efficient numerical methods within a general framework for solving such systems with moving free boundaries. The major numerical challenge is to track the moving free boundaries, especially for high spatial dimensions. To overcome this, a front tracking framework coupled with implicit solver is first introduced for the 2D model with radial symmetry. For the general 2D model, a level set approach is employed to more efficiently treat complicated topological changes. The accuracy and order of convergence for the proposed methods are discussed, and the numerical simulations agree well with theoretical results.
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