A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation

A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation

Year:    1998

Author:    Zhen Han, Longjun Shen

Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 129–140

Abstract

We construct and analyze a family of semi-discretized difference schemes with two parameters for the Korteweg-de Vries (KdV) equation. The scheme possesses the first four near-conserved quantities for periodic boundary conditions. The existence and the convergence of its global solution in Sobolev space $\boldsymbol{L}_{\infty} (0, T; \boldsymbol{H}^3)$ are proved and the scheme is also stable about initial values. Furthermore, the scheme conserves exactly the first two conserved quantities in the special case. 

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1998-JCM-9147

Journal of Computational Mathematics, Vol. 16 (1998), Iss. 2 : pp. 129–140

Published online:    1998-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Convergence difference scheme KdV equation conserved quantity.

Author Details

Zhen Han

Longjun Shen