二维定常对流扩散方程的重心插值配点法
Barycentric Interpolation Collocation Method for the Two-Dimensional Steady Convection-Diffusion Equation
摘要: 利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法，并给出微分矩阵。其次，离散二维定常对流扩散方程以及初边值条件，利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算，比较了两种边界条件施加方法下两种重心插值法的数值算法。数值算例表明了重心插值配点法的高精度性。
Abstract: The two-dimensional steady convection-diffusion equation is solved by barycentric interpolation method. Firstly, the two barycentric interpolation collocation methods are introduced, and the differential matrices are given. Secondly, the two-dimensional steady convection-diffusion equation and initial boundary conditions are dispersed, and the boundary conditions are treated by substitution and addition. Numerical calculations are carried out by using the second type of Chebyshev node and the equidistant node. Numerical examples demonstrate that this barycentric interpolation collocation method has high accuracy.
文章引用：李瑞, 宋灵宇. 二维定常对流扩散方程的重心插值配点法[J]. 理论数学, 2025, 15(4): 201-212. https://doi.org/10.12677/pm.2025.154123

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