新疆师范大学学报（自然科学版）2026，Vol.45Issue(1)：83-90,8.
Chebyshev谱法求解正则长波方程
The Solution of the Regularized Long Wave Equations Using the Chebyshev Spectral Method
摘要
Abstract
The regularized long wave equation is one of the most important nonlinear partial differential equations.In this paper,the Chebyshev spectral method is proposed to solve the regularized long wave equation,the Chebyshev polynomial and Chebyshev-Gauss-Lobatto are used to construct the derivative matrix,and the one-dimensional and two-dimensional regularized long wave equations are approximated as ordinary differential equations to prove the error estimation of the discrete Chebyshev spectral method and the solution is performed using a higher-order ODE solver.The numerical results obtained by the method are compared with the exact solution,and the effectiveness of the method is verified.The data results in this paper are more accurate than that of other methods.关键词
正则长波方程/Chebyshev谱法/Chebyshev-Gauss-Lobatto点/Chebyshev多项式Key words
Regularized long wave equation/Chebyshev spectral method/Chebyshev-Gauss-Lobatto point/Chebyshev polynomials分类
数理科学引用本文复制引用
罗妍,宋灵宇..Chebyshev谱法求解正则长波方程[J].新疆师范大学学报（自然科学版）,2026,45(1):83-90,8.基金项目
国家自然科学基金青年项目(12101482) （12101482）
中国博士后科学基金面上项目(2022M722604) （2022M722604）
陕西省科技厅重点研发一般资助项目(2023-YBSF-372). （2023-YBSF-372）
