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Linear Sixth-Order Conservation Difference Scheme for KdV Equation

Author

Listed:
  • Jie He

    (College of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, China)

  • Jinsong Hu

    (College of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, China)

  • Zhong Chen

    (Applied Nuclear Technology in Geosciences Key Laboratory of Sichuan, Chengdu University of Technology, Chengdu 610059, China)

Abstract

A numerical investigation is conducted for the initial boundary value problem of the Korteweg–de Vries (KdV) equation with homogeneous boundary conditions. Using the average implicit difference discretization, a second-order theoretical accuracy in time is achieved. For the spatial direction, a center-symmetric discretization coupled with the extrapolation technique is employed, yielding a three-level linear difference method with sixth-order accuracy. Consequently, the integration of these methods results in a linear finite difference scheme that accurately simulates the two conserved quantities of the original problem. Furthermore, theoretical results, including the convergence and stability of the proposed scheme, are proved using the discrete Sobolev inequality and the discrete Gronwall inequality. Numerical experiments validate the reliability of the scheme.

Suggested Citation

  • Jie He & Jinsong Hu & Zhong Chen, 2025. "Linear Sixth-Order Conservation Difference Scheme for KdV Equation," Mathematics, MDPI, vol. 13(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1132-:d:1623939
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