数值计算与计算机应用
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数值计算与计算机应用  2017, Vol. 38 Issue (4): 245-255    DOI:
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Klein-Gordon方程的紧致辛中点格式
尹秀玲1, 张静静2, 刘艳芹1, 郑晓彤3
1. 德州学院数学科学学院, 德州 253023;
2. 华东交通大学理学院, 南昌 330013;
3. 中国人民大学统计学院, 北京 100872
A COMPACTLY SYMPLECTIC MIDPOINT METHOD FOR THE KLEIN-GORDON EQUATION
Yin Xiuling1, Zhang Jingjing2, Liu Yanqin1, Zheng Xiaotong3
1. College of Mathematical Sciences, Dezhou University, Shandong 253023, China;
2. School of Science, East China Jiao Tong University, Nanchang 330013, China;
3. School of Statistics, Renmin University of China, Beijing 100872, China
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摘要 本文利用紧致算子和修正的辛中点格式构造了Klein-Gordon方程初值问题的保结构算法.该紧致辛中点格式在时间方向具有二阶精度,在空间方向具有六阶精度,保持离散的辛结构,是线性稳定的算法.另外,该算法保持线性系统的离散能量,而对非线性系统,该算法满足一个离散能量的转移公式.数值算例验证了理论分析.
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关键词Klein-Gordon方程   紧致算子   辛格式     
Abstract: This paper proposes a structure-preserving solver for the initial boundary value problem of the Klein-Gordon equation by using a compact operator and modified symplectic midpoint method. The solver possesses a discrete symplectic structure. It is linearly stable. In addition, the solver preserves a discrete energy for linear system, while for nonlinear system, it satisfies a discrete energy transit formula. Numerical example verifies the theoretical analysis.
Key wordsKlein-Gordon equation   Compact operator   Symplectic scheme.   
收稿日期: 2016-09-12;
基金资助:

国家自然科学基金青年项目(11501082,11201125);山东省自然科学基金项目(ZR2017MA050,ZR2016AQ07);山东省高等学校科技计划项目(J17KA156).

引用本文:   
. Klein-Gordon方程的紧致辛中点格式[J]. 数值计算与计算机应用, 2017, 38(4): 245-255.
. A COMPACTLY SYMPLECTIC MIDPOINT METHOD FOR THE KLEIN-GORDON EQUATION[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(4): 245-255.
 
[1] Wang Q F. Numerical solution for series sine-Gordon equations using variational method and finite element approximation[J]. Appl. Math. Comput., 2005, 168(1):567-599.
[2] Reich S. Muiti-Symplectic Runge-Kutta collocation methods for Hamiltonian wave equations[J]. J. Comput. Phys., 2000, 157:473-499.
[3] 王兰, 马院萍, 孔令华等. Klein-Gordon-Schrödinger方程的辛Fourier拟谱格式[J]. 计算物理, 2011, 28(2):275-282.
[4] Bridge T J, Reich S. Multi-symplectic integrators:numerical schemes for Hamiltonian PDEs that conserve symplectivity[J]. Phys. Let. A, 2001, 284:184-193.
[5] Wang Y S, Qin M Z. Multisymplectic structure and multisymplectic scheme for the nonlinear wave equation[J]. Acta Mathematicae Applicatae Sinica, 2002, 18(1):169-176.
[6] Wang Y S, Wang B. High-order multi-symplectic schemes for the nonlinear Klein-Gordon equation[J]. Appl. Math. Comput., 2005, 166(3):608-632.
[7] Li Q H, Sun Y J, Wang Y S. On multisymplectic integrators based on Runge-Kutta-Nyström methods for Hamiltonian wave equations[J]. Appl. Math. Comp., 2006, 182(2):1056-1063.
[8] Li H C, Sun J Q, Qin M Z. New explicit multi-symplectic scheme for nonlinear wave equation[J]. Appl. Math. Mechanics, 2014, 35(3):369-380.
[9] Sanz-Serna J M. An unconventional symplectic integrator of W[J]. Appl. Numer. Math., 1994, 16(1-2):245-250.
[10] Hairer E, Lubich C, Wanner G. Geometric numerical integration[M]. Springer Verlag, Berlin, 2006.
[11] Tang Y F, Cao J W, et al. Symplectic methods for the Ablowitz-Ladik discrete nonlinear Schrödinger equation[J]. J. Phys. A:Math. Theor., 2007, 40(10):2425-2437.
[12] Hong J L, Sun Y J. Generating functions of multi-symplectic RK methods via DW Hamilton-Jacobi equations[J]. Numerische Mathematik, 2008, 110(4):491-519.
[13] Marsden J E, Patrick G W, Shkoller S. Multisymplectic geometry, variational integrators, and nonlinear PDEs[J]. Commu. Math. Phys., 2010, 199(2):351-395.
[14] 徐金平, 单双荣. 带五次项的非线性Schrödinger方程的多辛Fourier拟谱算法[J]. 数值计算与计算机应用, 2010, 31(1):55-63. 浏览
[15] Zhu H J, Chen Y M, Song S H. Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations[J]. Appl. Numer. Math., 2011, 61(3):308-321.
[16] 李昊辰, 孙建强. 饱和非线性薛定愕方程多辛Euler-Box方法[J]. 数值计算与计算机应用, 2011, 32(3):220-228. 浏览
[17] McLachlan R I, Ryland B N, Sun Y J. High order multisymplectic Runge-Kutta methods[J]. SIAM J. Sci. Comput., 2014, 36(5):2199-2226.
[18] Zhang R L, Tang Y F, et al. Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems[J]. Science China Math., 2015, 59(2):1-18.
[19] 孔令华. 哈密尔顿系统的分裂步多辛数值积分(英文)[J]. 江西师范大学学报, 2015, 39(5):507-513.
[20] Lele S. Compact Finite Difference Schemes with Spectral-like Solution[J]. J. Comput. Phys., 1992, 103:16-42.
[21] Ma Y P, Kong L H, Hong J L. High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations. Comput. Math. Appl. 2011, 61:319-333.
[22] 王廷春. 求解非线性Schrödinger方程的一个线性化紧致差分格式[J]. 数值计算与计算机应用, 2012, 33(4):569-572.
[23] Wang Y S, Wang B, Qin M Z. Local structure-preserving algorithms for partial differential equations[J]. Science China, 2008, 51(11):2115-2136.
[24] 张静静. 基于精确数值离散的一类新的辛算法[J]. 江西师范大学学报, 2015, 39(6):588-591.
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