Multisymplectic Euler Box Scheme for the KdV Equation
WANG Yu-Shun 1,2, WANG Bin 2, CHEN Xin 1
1School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097
2Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
Multisymplectic Euler Box Scheme for the KdV Equation
WANG Yu-Shun 1,2;WANG Bin 2;CHEN Xin 1
1School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097
2Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
We investigate the multisymplectic Euler box scheme for the Korteweg--de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky- Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.
Abstract：We investigate the multisymplectic Euler box scheme for the Korteweg--de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky- Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.
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2007, Vol. 24 
