| 粱振动方程的多辛格式及其守恒律 |
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| 引用本文： | 曾文平,郑小红.粱振动方程的多辛格式及其守恒律[J].福州大学学报(自然科学版),2004,32(2):132-137. |
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| 作者姓名： | 曾文平 郑小红 |
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| 作者单位： | 华侨大学数学系,福建,泉州,362011 |
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| 基金项目： | 国务院侨办科研基金资助项目(02QZR07) |
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| 摘 要： | 提出了梁振动方程的一个新的多辛Hamilton形式,并用中点离散得到了一个新的等价于Preissman多辛积分的格式.进而证明它是无条件稳定且满足离散的多辛守恒律、局部能量守恒律及动量守恒律.最后以数值例子验证了理论分析的正确性.
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| 关 键 词： | 梁 振动方程 多辛 守恒律 稳定性 收敛性 |
| 文章编号： | 1000-2243(2004)02-0132-06 |
| 修稿时间： | 2003年7月7日 |
Multi-symplectic schemes and conservation laws for the vibration equation of beams |
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| ZENG Wen-ping,ZHENG Xiao-hong.Multi-symplectic schemes and conservation laws for the vibration equation of beams[J].Journal of Fuzhou University(Natural Science Edition),2004,32(2):132-137. |
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| Authors: | ZENG Wen-ping ZHENG Xiao-hong |
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| Institution: | (Department of mathematics, Huaqiao University, Quanzhou, Fujian 362011, China) |
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| Abstract: | We presend a new multi-symplectic Hamiltonian formulation for vibration equation of beams, and get a new scheme which is equivalent to the multi-symplectic Preissman integrator by discreting the equations with middle point formulations. Moreover, we prove that the new scheme is unconditional stable and convergence, and that it satisfies the conservation law of discrete multi-symplectic, discrete energy and discrete momentum. And the numerical experiments show the correctness of the theoretical analysis. |
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| Keywords: | beam vibration equation multi-symplectic conservation law stability convergence |
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