数值方法求解微分方程的研究——基于切比雪夫多项式的谱方法
Research on Solving Differential Equations by Numerical Method—Spectral Methods Based on Chebyshev Polynomials
DOI: 10.12677/PM.2024.141016, PDF,   
作者: 赵 远：云南财经大学，统计与数学学院，云南 昆明
关键词: 谱方法；切比雪夫多项式；偏微分方程求解；Spectral Method； Chebyshev Polynomials； Solution of PDE
摘要: 谱方法是处理微分方程的常用方法，本文以理论完善的谱方法为基础，详细介绍了切比雪夫多项式通过S-L问题的由来与切比雪夫多项式的部分性质，并利用这些性质将这些正交多项式作为基对函数进行展开，从而数值求解偏微分方程，我们利用案例来展现其具体的运算过程并验证其方法的有效性。
Abstract: Based on Spectral Method, we introduce the origin of Chebyshev polynomials via S-L problems and some properties of Chebyshev polynomials. With these properties, we use these orthogonal poly-nomials as basic functions to solve partial differential equations. Also, we use examples to show the detailed operations and verify its effectiveness.
文章引用：赵远. 数值方法求解微分方程的研究——基于切比雪夫多项式的谱方法[J]. 理论数学, 2024, 14(1): 153-161. https://doi.org/10.12677/PM.2024.141016

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