Chinese Quarterly Journal of Mathematics

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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, Luyang 471000,
    China
  • Received:2022-04-20 Online:2023-04-12 Published:2023-04-12
  • Contact: WANG Chuan (1995-), male, native of Shangqiu, Henan, postgraduate student of Henan University of Science and Technology, engages in numerical solutions of partial equations; 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 partial equations; 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: