计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  在线办公 | 
计算数学  2018, Vol. 40 Issue (3): 313-324    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
非线性耦合Schrödinger-KdV方程组的一个局部能量守恒格式
郭峰
华侨大学数学科学学院, 泉州 362021
A LOCAL ENERGY CONSERVATIVE SCHEME FOR NONLINEAR COUPLED SCHRÖDINGER-KDV EQUATIONS
Guo Feng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
 全文: PDF (922 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文利用平均值离散梯度给出了一个构造哈密尔顿偏微分方程的局部能量守恒格式的系统方法.并用非线性耦合Schrödinger-KdV方程组加以说明.证明了格式满足离散的局部能量守恒律,在周期边界条件下,格式也保持离散整体能量及系统的其它两个不变量.最后数值实验验证了理论结果的正确性.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词耦合Schrö   dinger-KdV方程组   局部能量守恒律   平均值离散梯度     
Abstract: In this paper, by using the mean value discrete gradient, we give a systematic method to construct a local energy conservative scheme for Hamiltonian PDEs. This method is illustrated by nonlinear coupled Schrödinger-KdV equations. We prove that the scheme satisfies the discrete local energy conservation law, with the periodic boundary conditions, the scheme also conserves the discrete global energy and other two invariants. Finally, Numerical experiments are presented to verify the accuracy of theoretical results.
Key wordscoupled Schrödinger-KdV equations   local enery conservation law   the mean value discrete gradient   
收稿日期: 2017-08-30;
引用本文:   
. 非线性耦合Schrödinger-KdV方程组的一个局部能量守恒格式[J]. 计算数学, 2018, 40(3): 313-324.
. A LOCAL ENERGY CONSERVATIVE SCHEME FOR NONLINEAR COUPLED SCHRÖDINGER-KDV EQUATIONS[J]. Mathematica Numerica Sinica, 2018, 40(3): 313-324.
 
[1] Appert K,Vaclavik J.Dynamics of coupled solitons[J].Physics of Fluids,1977,11(20):1845-1849.
[2] Zhu P F,Kong L H,Wang L.The conservation laws of Schrödinger-KdV equations[J].J Jiangxi Normal Univ,2012,36(5):495-498.
[3] Abdou M A,Soliman A A.New applications of variational iteration method[J].Physica D-Nonlinear Phenomena,2005,211(1-2):1-8.
[4] Golbabai A,Safdari-Vaighani A.A meshless method for numerical solution of the coupled Schrödinger-KdV equations[J].Computing,2011,92(3):225-242.
[5] 王兰,段雅丽,孔令华.长短波方程多辛数值模拟(英文)[J].中国科学技术大学学报,2015,45(9):721-726.
[6] Liu Y Q,Cheng R J,Ge H X.An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations[J].Chinese Physics B,2013,22(10):100204.
[7] Bai D M,Zhang L M.The finite element method for the coupled Schrödinger-KdV equations[J].Physics Letters A,2009,373(26):2237-2244.
[8] Zhang H,Song S H,Chen X D,Zhou W E.Average vector field methods for the coupled Schrödinger-KdV equations[J].Chinese Physics B,2014,23(7):070208.
[9] Feng K,Qin M Z.The symplectic methods for the computation of hamiltonian equations,Lecture Notes in Mathematics[M].Berlin,Heidelberg:Springer,1987:1-37.
[10] Feng K,Qin M Z.Symplectic Geometric Algorithms for Hamiltonian Systems[M].Heidelberg:Springer and Zhejiang Science and Technology Publishing House,2010.
[11] Bridges T J.Multi-symplectic structures and wave propagation[J].Mathematical Proceedings of the Cambridge Philosophical Society,1997,121(1):147-190.
[12] Shang Z J.KAM theorem of symplectic algorithms for Hamiltonian systems[J].Numerische Mathematik,1999,83(3):477-496.
[13] Reich S.Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations[J].Journal of Computational Physics,2000,157(2):473-499.
[14] Hairer E,Lubich C,Wanner G.Geometric Numerical Integration:Structure Preserving Algorithms for Ordinary Differential Equations[M].Berlin:Springer-Verlag,2002.
[15] Hong J L,Li C.Multi-symplectic Runge-Kutta methods for nonlinear dirac equations[J].Journal of Computational Physics,2006,211(2):448-472.
[16] Liu H Y,Zhang K.Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations[J].Ima Journal of Numerical Analysis,2006,26(2):252-271.
[17] Hong J L,Liu H Y,Sun G.The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDES[J].Mathematics of Computation,2006,75(253):167-181.
[18] Kong L H,Hong J L,Zhang J J.Splitting multisymplectic integrators for Maxwell's equations[J].Journal of Computational Physics,2010,229(11):4259-4278.
[19] Sun Y,Tse P S P.Symplectic and multisymplectic numerical methods for Maxwell's equations[J].Journal of Computational Physics,2011,230(5):2076-2094.
[20] Wang Y S,Hong J L.Multi-symplectic algorithms for Hamiltonian partial differential equations[J].Commun.Appl.Math.Comput.,2013,27(2):163-230.
[21] Marsden J E,Patrick G W,Shkoller S.Multisymplectic geometry,variational integrators,and nonlinear PDEs[J].Communications in Mathematical Physics,1998,199(2):351-395.
[22] Bridges T J,Reich S.Multi-symplectic integrators:numerical schemes for Hamiltonian PDEs that conserve symplecticity[J].Physics Letters A,2001,284(4-5):184-193.
[23] Wang Y S,Wang B,Ji Z Z.Structure Preserving Algorithms for Soliton Equations[J].Chinese Journal of Computational Physics,2004,21(5):386-400.
[24] Wang Y S,Wang B,Qin M Z.Local structure-preserving algorithms for partial differential equations[J].Science in China Series a-Mathematics,2008,51(11):2115-2136.
[25] 董洪泗.两类非线性Schrödinger方程的局部保结构算法[D].南京师范大学,2009.
[26] 孙丽平.局部保结构算法的复合构造[D].南京师范大学,2010.
[27] Harten A,Lax P D,Van Leer B.On upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws[J].SIAM Rev., 1983,25(1):35-61.
[28] Itoh T,Abe K.Hamiltonian-conserving discrete canonical equations based on variational difference quotients[J].J.Comput.Phys.,1988,76(1):85-102.
[29] 张善卿,李志斌.非线性耦合Schrödinger-KdV方程组新的精确解析解[J].物理学报,2002,51(10):2197-2201.
[30] 王廷春.某些非线性孤立波方程(组)的数值算法研究[D].南京航空航天大学,2008.
没有找到本文相关文献

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10