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Volume 16, Issue 2
A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation

Zhen Han & Longjun Shen

J. Comp. Math., 16 (1998), pp. 129-140.

Published online: 1998-04

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  • 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. 

  • Keywords

Convergence, difference scheme, KdV equation, conserved quantity.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-129, author = {Han , Zhen and Shen , Longjun}, title = {A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {2}, pages = {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. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9147.html} }
TY - JOUR T1 - A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation AU - Han , Zhen AU - Shen , Longjun JO - Journal of Computational Mathematics VL - 2 SP - 129 EP - 140 PY - 1998 DA - 1998/04 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9147.html KW - Convergence, difference scheme, KdV equation, conserved quantity. AB -

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. 

Zhen Han & Longjun Shen. (1970). A Family of Difference Schemes with Four Near-Conserved Quantities for the KdV Equation. Journal of Computational Mathematics. 16 (2). 129-140. doi:
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