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2维Schrdinger方程的多辛格式 被引量：4

Multisymplectic Integrator for Two-Dimensional Schrdinger Equation
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摘要 利用Lengdre变换构造了2维Schrdinger方程的多辛形式,对它在时空方向都利用Euler中点格式离散得到了一个2阶多辛格式.理论分析表明格式是保持系统的电荷守恒和能量守恒,且无条件稳定2阶收敛的数值实验验证了理论分析的正确性和多辛格式的优越性. A multisymplectic formulism is constructed for two-dimensinal Schrdinger equation by Lengdre transformation.It is approximated by Euler midpoint rule in both time and space directions which yields a second-order multisymplectic scheme.It suggests that the scheme can preserve the charge and energy invariants in theory.Moreover,it is unconditionally stable and second-order convergence rate.Numerical experiments verify the correctness of theoretical analysis and the superior of multisymplectic schemes.
作者 王兰 陈静
机构地区 江西师范大学数学与信息科学学院 江西农业大学理学院
出处 《江西师范大学学报（自然科学版）》 CAS 北大核心 2010年第6期600-603,608,共5页 Journal of Jiangxi Normal University(Natural Science Edition)
基金 国家自然科学基金(10901074) 江西省自然科学基金(2008GQS0054) 江西省教育厅基金(GJJ09147) 江西师范大学2008年与2010年青年成长基金 江西农业大学2009年青年基金资助项目
关键词 2维Schrdinger方程 多辛格式 守恒律 哈密尔顿系统 two-dimensional Schrdinger equation multisymplectic scheme conservation law hamiltonian system
分类号 O241.8 [理学—计算数学]
  • 相关文献

参考文献10

  • 1Feng Kang.On difference schemes and symplectic geometry[C]//Feng Kang.Proceeding of the 1984 Beijing Symposium on Diffetential Geomerry and Differential Equations Computation of Partial Differential Equations.Beijing:Science Press,1985:42-58.
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二级参考文献10

  • 1黄浪扬.非线性Pochhammer-Chree方程的多辛格式[J].计算数学,2005,27(1):96-100. 被引量：5
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共引文献14

同被引文献20

  • 1刘常福.一类长短波方程的新的精确解[J].西南师范大学学报（自然科学版）,2005,30(3):409-413. 被引量：4
  • 2谢绍龙,王林.一类三阶非线性偏微分方程的孤立波[J].江西师范大学学报（自然科学版）,2006,30(4):311-314. 被引量：2
  • 3Perez-Garcia V M, Liu Xiaoyuan. Numerical methods for the simulation of trapped nonlinear SchrSdinger system [J]. Appl Math Comput, 2003, 144(2/3): 215-235.
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  • 6Hong Jianlin, Kong Linghua. Novel multi-symplectic integrators for nonlinear fourth-order Schrtidinger equation with a trapped term [J]. Commun Comput Phys,2010, 7(3): 613-630.
  • 7Kong Linghua, Hong Jianlin, Zhang Jingjing. Splitting multisymplectic methods for Maxwell's equation [J]. J Comput Phys, 2010, 229(11): 4259-4278.
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  • 9Ogawa T. Global well-posedness and conservation laws for the water wave interaction equation [J].Proc Royal Soc,Edinburgh, 1997, 127(2): 369-384.
  • 10Chang Qianshun, Wong Y S, Lin Chikun. Numerical computations for long-wave short-wave interaction equations in semi-classical limit [J]. J Comput Phys, 2008, 227(19): 8489-8507.

引证文献4

二级引证文献15

江西师范大学学报（自然科学版）
2010年 第6期

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