Chinese Quarterly Journal of Mathematics ›› 2023, Vol. 38 ›› Issue (4): 392-400.doi: 10.13371/j.cnki.chin.q.j.m.2023.04.006

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

  

  1. 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).

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

CLC Number: