Linear Sixth-Order Conservation Difference Scheme for KdV Equation

Jie He, Jinsong Hu () and Zhong Chen
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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

Mathematics, 2025, vol. 13, issue 7, 1-16

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.

Keywords: KdV equation; three level; high accuracy; conservation; convergence; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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