求解广义Burgers-Fisher方程的微分求积法  

Differential quadrature method for solving the generalized Burgers-Fisher equations

作　　者：阿迪力·艾力 开依沙尔·热合曼[1] Adil ALI;Kaysar RAHMAN(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,Xinjiang,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《山东大学学报（理学版）》2024年第10期30-39,共10页Journal of Shandong University(Natural Science)

基　　金：新疆大学博士启动基金项目(BS150204)。

摘　　要：对Dirichlet边界和Neumann边界条件下的广义Burgers-Fisher方程构造了高精度数值计算格式。首先,空间上分别采取均匀网格和Chebyshev-Gauss-Lobatto网格的拉格朗日插值多项式微分求积法,时间上采取三阶强稳定性保持Runge-Kutta格式;其次,利用矩阵方法进行稳定性分析;最后,对2种不同边界条件下的数值例子进行数值计算,并将结果和其他数值方法进行比较,验证本文格式的有效性。In this paper,a high accuracy numerical scheme is constructed for the generalized Burgers-Fisher equation with Dirichlet boundary or Neumann boundary conditions.Firstly,the Lagrange interpolation polynomial differential quadrature method with uniform grid and Chebyshev-Gauss-Lobatto grid is used in space,and the third-order strong stability-preserving Runge-Kutta scheme is used in time.Secondly,the stability of the scheme is analyzed by using the matrix method.Finally,two numerical examples with different boundary conditions are calculated,and the results are compared with other numerical methods to verify the effectiveness of the proposed scheme.

关 键 词：广义BURGERS-FISHER方程 微分求积法 Chebyshev-Gauss-Lobatto网格 强稳定性保持Runge-Kutta格式 

分 类 号：O241[理学—计算数学]