Chebyshev谱法求解电报方程
Chebyshev Spectral Method for Solving Telegraph Equation
摘要: 双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法，采用Chebyshev-Gauss-Lobatto配点，利用Chebyshev多项式构造导数矩阵，将电报方程近似为常微分方程，证明了电报方程的离散Chebyshev谱法的误差估计，采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较，验证了方法的有效性，数据结果的误差与其他方法相比有较高的精确度。
Abstract: Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.
文章引用：罗妍, 宋灵宇. Chebyshev谱法求解电报方程[J]. 应用数学进展, 2025, 14(4): 614-624. https://doi.org/10.12677/aam.2025.144191

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