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.