| Dirac方程的多辛格式 |
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| 引用本文： | 王健.Dirac方程的多辛格式[J].上海交通大学学报,2004,38(5):849-852. |
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| 作者姓名： | 王健 |
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| 作者单位： | 上海交通大学,数学系,上海,200240 |
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| 摘 要： | 基于Bridges原理，得到了1 1维Dirac方程的多辛哈密尔顿系统形式及局部守恒律。空间方向采用Fourier拟谱格式，时间方向为中点辛格式，得到的多辛半离散和全离散格式满足局部多辛守恒,证明了波函数模方和局部能量守恒。数值结果表明了算法的长时间有效性。
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| 关 键 词： | 多辛格式 局部守恒律 Fourier拟谱格式 Dirac方程 |
| 文章编号： | 1006-2467(2004)05-0849-04 |
| 修稿时间： | 2003年3月25日 |
Multi-symplectic Method for the Dirac Equation |
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| WANG Jian.Multi-symplectic Method for the Dirac Equation[J].Journal of Shanghai Jiaotong University,2004,38(5):849-852. |
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| Authors: | WANG Jian |
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| Abstract: | Based on Bridges's principle, the multi-symplectic form of 1+1 dimension Dirac equation and local conservation laws were obtained. The Fourier pseudospectral discretization in space and the midpoint symplectic discretization in time are considered. Both the multi-symplectic semi-discretization and full-discretization satisfy the local conservation laws. The conservation of the modul of wavefunction and local energy was proved. Numerical results were also reported to show the long time effectiveness of the schemes. |
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| Keywords: | multi-symplectic local conservation laws Fourier pseudospectral Dirac equation |
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