%0 Journal Article
%T 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<br>Research on Solving Differential Equations by Numerical Method—Spectral Methods Based on Chebyshev Polynomials
%A 赵远
%J Pure Mathematics
%P 153-161
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/PM.2024.141016
%X 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。<br />
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.
%K 谱方法，切比雪夫多项式，偏微分方程求解<br>Spectral Method
%K Chebyshev Polynomials
%K Solution of PDE
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=79555