Korteweg-de Vries方程的Legendre时空谱配置方法

doi:10.13371/j.cnki.chin.q.j.m.2023.04.006

数学季刊 ›› 2023, Vol. 38 ›› Issue (4): 392-400.doi: 10.13371/j.cnki.chin.q.j.m.2023.04.006

Korteweg-de Vries方程的Legendre时空谱配置方法

School of Mathematics and Statistics, Henan University of Science and Technology,
Luoyang 471000, China

收稿日期:2022-04-20 出版日期:2023-12-30 发布日期:2023-12-15
通讯作者: WANG Chuan (1995-), male, native of Shangqiu, Henan, postgraduate student of Henan University of Science and Technology, engages in numerical solutions of PDEs; E-mail: c_wang2022@163.com
作者简介:WANG Chuan (1995-), male, native of Shangqiu, Henan, postgraduate student of Henan University of Science and Technology, engages in numerical solutions of PDEs; QIAO Yan (2000-), female, native of Zhumadian, Henan, undergraduate student of Henan University of Science and Technology.
基金资助:
Supported by National Natural Science Foundation of China (Grant Nos. 11771299, 11371123) and Natural Science Foundation of Henan Province (Grant No. 202300410156).

Space-Time Legendre Spectral Collocation Methods for Korteweg-De Vries Equation

School of Mathematics and Statistics, Henan University of Science and Technology,
Luoyang 471000, China

Received:2022-04-20 Online:2023-12-30 Published:2023-12-15
Contact: WANG Chuan (1995-), male, native of Shangqiu, Henan, postgraduate student of Henan University of Science and Technology, engages in numerical solutions of PDEs; E-mail: c_wang2022@163.com
About author:WANG Chuan (1995-), male, native of Shangqiu, Henan, postgraduate student of Henan University of Science and Technology, engages in numerical solutions of PDEs; QIAO Yan (2000-), female, native of Zhumadian, Henan, undergraduate student of Henan University of Science and Technology.
Supported by:
Supported by National Natural Science Foundation of China (Grant Nos. 11771299, 11371123) and Natural Science Foundation of Henan Province (Grant No. 202300410156).

摘要/Abstract

摘要： A Legendre-Legendre spectral collocation scheme is constructed for Korteweg-de Vries (KdV) equation on bounded domain by using the Legendre collocation method in both time and space, which is a nonlinear matrix equation that is changed to a nonlinear systems and can be solved by the usual fixed point iteration. Numerical results demonstrate the efficiency of the method and spectral accuracy.

关键词: Korteweg-de Vries equation, Space-time Legendre spectral collocation method, Initial-boundary value problem

Abstract: A Legendre-Legendre spectral collocation scheme is constructed for Korteweg-de Vries (KdV) equation on bounded domain by using the Legendre collocation method in both time and space, which is a nonlinear matrix equation that is changed to a nonlinear systems and can be solved by the usual fixed point iteration. Numerical results demonstrate the efficiency of the method and spectral accuracy.

Key words: Korteweg-de Vries equation, Space-time Legendre spectral collocation method, Initial-boundary value problem

中图分类号:

O175.2

王川, 乔炎. Korteweg-de Vries方程的Legendre时空谱配置方法[J]. 数学季刊, 2023, 38(4): 392-400.

WANG Chuan, QIAO Yan. Space-Time Legendre Spectral Collocation Methods for Korteweg-De Vries Equation[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 392-400.

Korteweg-de Vries方程的Legendre时空谱配置方法

Space-Time Legendre Spectral Collocation Methods for Korteweg-De Vries Equation

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