基于Chebyshev点的B样条配置法在奇异摄动两点边值问题中的应用研究
Study on Application of Chebyshev B-Spline Collocation Method on Singularly Perturbed Two-Point Boundary Value Problems
摘要: 在求解奇异摄动两点边值问题时，本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数，利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动扩散反应问题、奇异摄动对流扩散反应问题这两个算例的研究，表明基于Chebyshev点的B样条配置法与等距节点下的B样条配置法相比，前者具有高精度和高效率的优势。
Abstract: In solving the singular perturbation two-point boundary value problems, this paper constructs a Chebyshev B-spline collocation method. This method uses cubic B-spline functions as basis functions and utilizes the Chebyshev point as the configuration point to solve the equation directly. The specific steps in the implementation of the method and several details that need to be noted are discussed in the paper. Through the study of two arithmetic cases, namely, the singular regent diffusion response problem and the singular regent convection diffusion response problem, it is shown that the Chebyshev B-spline collocation method has the advantages of high accuracy and high efficiency as compared with the B-spline configuration method under equidistant nodes.
文章引用：韩梦如, 郭子磊, 赵运晓, 易佳雄, 陈璐瑶. 基于Chebyshev点的B样条配置法在奇异摄动两点边值问题中的应用研究[J]. 应用数学进展, 2025, 14(5): 262-273. https://doi.org/10.12677/aam.2025.145254

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