参考文献/References:
[1] Feng Kang.On difference schemes and symplectic geometry [C].Beijing:Science Press,1985:42-58.
[2] Feng Kang,Qin Mengzhao.Symplectic geometric algorithms for Hamiltonian systems [M].Heidelberg:Springer and Zhejiang Science and Technology Publishing House,2010.
[3] Hairer E,Lubich C,Wanner G.Geometric numerical integration:Structure preserving algorithms for ordinary diffenential equations [M].2nd ed.Berlin:Springer-Verlag,2006.
[4] Bridges T J,Reich S.Multi-symplectic integrators:numerical schemes for Hamiltonian PDEs that cssonserve symplecticity [J].Phys Lett A 2001,284(4):184-193.
[5] Marsden J,Patrick G,Shkoller S.Mulltisymplectic geometry,variational integrators,and nonlinear PDEs [J].Comm Math Phys,1998,199(2):351-395.
[6] Reich S.Multi-symplectic Runge-Kutta method for Hamiltonian wave equations [J].J Comput Phys,2000,157(2):473-499.
[7] Hong Jialin,Li Chun.Multi-symplectic Runge-Kutta methods for nonlinear dirac equations [J].J Comput Phys,2006,211(2):448-472.
[8] Hong Jialin,Liu Hongyu,Sun Geng.The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs [J].Math Comput,2006,75(253):167-181.
[9] Qin Mengzhao,Wang Yushun.Structure-preserving algorithm for partial differential equation [M].Hangzhou:Zhejiang Science and Technology Publishing House,2013.
[10] Wang Yushun,Hong Jialin.Multi-symplectic algorithms for Hamiltonian partial differential equations [J].Commun Appl Math & Comput,2013,27(2):163-230.
[11] Hong Jialin,Kong Linghua.Novel multisymplectic integrators for nonlinear fourth-order Schrödinger equation with trapped term [J].Commun Comput Phys,2010,7(3):613-630.
[12] Kong Linghua,Hong Jialin,Zhang Jingjing.Splitting multi-symplectic methods for Maxwell's equation [J].J Comput Phys,2010,229(11):4259-4278.
[13] Kong Linghua,Hong Jialin,Zhang Jingjing.LOD-MS for Gross-Pitaevskii equation in Bose-Einstein condensates [J].Commun Comput Phys,2013,14(1):219-214.
[14] Zhu Huajun,Chen Yaming,Song Songhe,et al.Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations [J].Appl Numer Math,2011,61(3):308-321.
[15] Ma Yuanping,Kong Linghua,Hong Jialin,et al.High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations [J].Comput & Math with Appl,2011,61(2):319-333.
[16] Kong Linghua,Cao Ying,Wang Lan.Split-step multisymplectic integrator for the fourth-order Schrödinger equation with cubic nonlinear term [J].Chin J Comput Phys,2011,28(5):76-82.
[17] Tong Hui,Kong Linghua,Wang Lan.Compact splitting multisymplectic scheme for Dirac equation [J].J Jiangxi Normal Univer,2014,38(5):521-525.
[18] Huang Hong,Wang Lan.Local one-dimensional multisymplectic integrator for Schrödinger equation [J].J Jiangxi Normal Univer,2011,35(5):455-458.
[19] Wang Lan,Fu Fangfang,Tong Hui.The split-step multisymplectic scheme for Dirac equation [J].J Jiangxi Normal Univer,2013,37(5):462-465.
[20] Zhou Wenying,Kong Linghua,Wang Lan.The energy identities of the local one dimensional multisymplectic scheme for 3-D Maxwell's equation [J].J Jiangxi Normal Univer,2015,39(1):55-58.
相似文献/References:
[1]童慧,孔令华,王兰.Dirac方程的紧致分裂多辛格式[J].江西师范大学学报(自然科学版),2014,(05):521.
TONG Hui,KONG Ling-hua,WANG Lan.Compact Splitting Multisymplectic Scheme for Dirac Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(05):521.