半直线上Kortewego-de Vries方程的Laguerre谱配置方法
Generalized Laguerre Spectral-Collocation Method for KdV Equations on the Half Line
摘要: 以Laguerre-Gauss-Radau节点为配置点，用带松弛因子的Lagrange插值函数逼近半直线上的Kortewego-de Vries方程初边值问题的理论解，给出算法格式和相应的数值结果，表明所提算法格式的有效性和高精度。对理论解中参数的不同取值，通过适当地选择插值函数中的松弛因子，数值解可以很好地匹配理论解，而且所给算法对长时间的计算仍然有效。
Abstract: Interpolation function approximations with relaxation factor by using Laguerre-Gauss-Radau nodes as collocation points to the Korteweg-de Vries equation on semi-infinite intervals are considered. The validity and high accuracy of the proposed algorithm are demonstrated. By choosing the relaxation factor of the interpolation function properly, the numerical solution can match the theoretical solution well, and the algorithm is still valid for a long time.
文章引用：王其霞, 苗伊浩, 王天军. 半直线上Kortewego-de Vries方程的Laguerre谱配置方法[J]. 应用数学进展, 2020, 9(9): 1583-1588. https://doi.org/10.12677/AAM.2020.99186

参考文献

[1] Korteweg, D. and De Vries, G. (1895) On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. Philosophical Magazine, 39, 422-443. [Google Scholar] [CrossRef] 
[2] Kawahara, R. (1972) Oscillatory Solitary Waves in Dispersive Media. Journal of the Physical Society of Japan, 33, 260-264. [Google Scholar] [CrossRef] 
[3] Kichenassamy, S. and Olver, P.J. (1992) Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations. SIAM Journal on Mathematical Analysis, 23, 1141-1166. [Google Scholar] [CrossRef] 
[4] 程斌. 用 Petrov-Galerkin 有限元法数值模拟 KdV方程[J]. 数值计算与计算机应用, 1992, 13(1): 73-80.
[5] Shen, J. (2003) A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KdV Equation. SIAM Journal on Numerical Analysis, 41, 1595-1619. [Google Scholar] [CrossRef] 
[6] Aksan, E.N. and Zdes, A. (2006) Numerical Solution of Korteweg-De Vries Equation by Galerkin B-Spline Finite Element Method. Applied Mathematics and Computation, 175, 1256-1265. [Google Scholar] [CrossRef] 
[7] 李冰冰, 王天军. Kortewego-Devries 方程的Hermite函数谱配置方法[J]. 应用数学进展, 2019, 8(4): 631-637.
[8] 贾红丽, 王中庆. KdV方程的Chebyshev-Hermite谱配置法[J]. 应用数学与计算数学学报, 2013, 27(1): 1-8.
[9] 王天军. 半无界非线性热传导方程的Laguerre拟谱方法[J]. 应用数学与计算数学学报, 2013, 27(1): 9-15.
[10] Shen, J., Tang, T. and Wang, L.L. (2011) Spectral Mathod: Algorithms, Analysis and Applications. Springer-Verlag, Berlin.
[11] Shen, J. and Tang, T. (2006) Spectral and High-Order Methods with Applications. Science Press, Beijing.

为你推荐