一维扩展的Fisher-Kolmogorov方程的BDF2-直接间断Galerkin算法
The BDF2-Direct Discontinuous Galerkin Algorithm for One-Dimensional Extended Fisher-Kolmogorov Equation
DOI: 10.12677/aam.2025.144200, PDF,   
作者: 王春娇, 王 蕾*：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: EFK；直接间断Galerkin；BDF2；EFK； Direct Discontinuous Galerkin； BDF2
摘要: 本文主要研究一维扩展的Fisher-Kolmogorov方程的有效数值算法。通过结合BDF2时间离散格式与直接间断有限元算法对一维扩展的Fisher-Kolmogorov方程进行求解。首先，引入辅助变量，将四阶的扩展的Fisher-Kolmogorov方程转化为低阶耦合方程，然后利用直接间断有限元求解耦合方程，最后使用BDF2方法，对时间格式进行离散。本文给出了详细的数值算法，并通过一个一维算例进行数值试验，验证了算法的有效性和收敛性。
Abstract: This paper mainly studies the effective numerical algorithm for the one-dimensional extended Fisher-Kolmogorov equation. By combining the BDF2 time discretization format with the direct discontinuous finite element algorithm, the one-dimensional extended Fisher-Kolmogorov equation is solved. Firstly, an auxiliary variable is introduced to transform the fourth-order extended Fisher-Kolmogorov equation into a low-order coupled equation. Then, the coupled equation is solved by using the direct discontinuous finite element method. Finally, the BDF2 method is used to discretize the time scheme. The detailed numerical algorithm is presented in this paper, and a one-dimensional example is used for numerical experiments to verify the effectiveness and convergence of the algorithm.
文章引用：王春娇, 王蕾. 一维扩展的Fisher-Kolmogorov方程的BDF2-直接间断Galerkin算法[J]. 应用数学进展, 2025, 14(4): 721-730. https://doi.org/10.12677/aam.2025.144200

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