吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (4): 878-885.

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二阶非线性抛物方程的B样条有限元法

秦丹丹1, 王大铭1, 黄文竹2   

  1. 1. 空军航空大学 基础部, 长春 130022; 2. 贵州医科大学 生物与工程学院, 贵阳 550025
  • 收稿日期:2023-12-01 出版日期:2024-07-26 发布日期:2024-07-26
  • 通讯作者: 黄文竹 E-mail:hwenzhu@gmc.edu.cn

B-Spline Finite Element Method of Second Order Nonlinear Parabolic Equation

QIN Dandan1, WANG Daming1, HUANG Wenzhu2   

  1. 1. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;
    2. School of Biology and Engineering, Guizhou Medical University, Guiyang 550025, China
  • Received:2023-12-01 Online:2024-07-26 Published:2024-07-26

摘要: 首先, 用二次B样条有限元法求解Fisher-Kolmogorov(FK)方程, 证明半离散格式与全离散格式解的稳定性与收敛性; 其次, 用Crank-Nicolson方法离散时间变量, 得到近似解的收敛阶为O((Δt)2+h3); 最后, 用数值算例验证了理论分析结果及B样条有限元法的有效性.

关键词: Fisher-Kolmogorov方程, 二次B样条有限元法, 稳定性, 收敛性

Abstract: Firstly, we uesd the quadratic B-spline finite element method to solve the Fisher-Kolmogorov (FK) equation, and proved the stability and convergence of solutions for the semi-discrete scheme and the fully discrete scheme. Secondly, the time variable was discretized by using the Crank-Nicolson method and the convergence order of the approximate solution was O((Δt)2+h3). Finally, the numerical example verified theoretical analysis results and the effectiveness of the B-spline finite element method.

Key words: Fisher-Kolmogorov equation, quadratic B-spline finite element method, stability, convergence

中图分类号: 

  • O241.82