数学季刊 >

2023 , Vol. 38 >Issue 4: 392 - 400

DOI: https://doi.org/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

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

收稿日期: 2022-04-20

  网络出版日期: 2023-12-15

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).

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

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

Received date: 2022-04-20

  Online published: 2023-12-15

Supported by

Supported by National Natural Science Foundation of China (Grant Nos. 11771299, 11371123) and Natural Science Foundation of Henan Province (Grant No. 202300410156).

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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

本文引用格式

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

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

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