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

WANG Chuan, QIAO Yan

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

Chinese Quarterly Journal of Mathematics >

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

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.04.006

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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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

Cite this article

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

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