2021-08-20 12:08

1. 毕业设计(论文)主要目标:

  1. 给出KGS方程的一个两层紧致差分格式,并证明该格式满足守恒率
  2. 误差分析
  3. 数值实验

2. 毕业设计(论文)主要内容:

  1. 给出KGS方程的一个两层紧致差分格式
  2. 证明给出的格式满足质量守恒和能量守恒
  3. 讨论格式的收敛性,求得局部误差
  4. 进行一些数值实验来测试理论分析所给出的紧致差分格式

3. 主要参考文献

[1] Fukuda I. and Tsutsumi M., On coupled Klein-Gordon-Schrodinger equations II, J. Math.Anal. Appl., 66 (1978) 358-378.[2] Makhankov V., Dynamics of classical solitons (in non-integrable systems), Phys. Lett. C.,35 (1978) 1-12.[3] Guo B., Global solution for some problem of a class of equations in interaction of complex

Schrodinger eld and real Klein-Gordon eld, Sci. China. Series. A., 2 (1982) 97-107.

[4] Hayashi N. and Wahl W., On the global strong solutions of coupled Klein-Gordon-Schrodinger equations, J. Math. Soc. Jpn., 39 (1987) 489-497.[5] Ozawa T. and Tsutsumi Y., Asymptotic behaviour of solutions for the coupled Klein-Gordon-Schrodinger equations, Adv. Stud. Pure. Math., 23 (1994) 295-305.[6] Ohta M., Stability of stationary states for the coupled Klein-Gordon-Schrodinger equations,Non. Anal., 27 (1996) 455-461.[7] Xia J., Han S. and Wang M., The exact solitary wave solution for the Klein-Gordon-Schrodinger, Appl. Math. Mech., 23 (2002) 52-58.[8] Wang M. and Zhou Y., The periodic wave solutions for the Klein-Gordon-Schrodingerequations, Phys. Lett. A., 318 (2003) 84-92.[9] Hioe F., Periodic solitary waves for two coupled nonlinear Klein-Gordon and Schrodingerequations, J. Phys. A: Math. Gen., 36 (2003) 7307-7330.[10] Darwish A. and Fan E., A series of new explicit exact solutions for the coupled Klein-Gordon-Schrodinger equations, Chaos. Soliton. Fract., 20 (2004) 609-617.[11] Xiang X., Spectral method for solving the system of equations of Schrodinger-Klein-Gordoneld, J. Comput. Appl. Math., 21 (1988) 161-171.[12] Bao W. and Yang L., Effcient and accurate numerical methods for the Klein-Gordon-Schrodinger equations, J. Comput. phys., 225 (2007) 1863-1893.[13] Kong L., Liu R. and Xu Z., Numerical simulation of interaction between Schrodinger eldand Klein-Gordon eld by multisymplectic method, Appl. Math. Comput., 181 (2006) 342-350.[14] Hong J., Jiang S. and Li C., Explicit multi-symplectic methods for Klein-Gordon-Schrodinger equations, J. Comput. Phys., 228 (2009) 3517-3532.[15] Kong L., Wang L., Jiang S. and Duan Y., Multisymplectic Fourier pseudo-spectral integratorsfor Klein-Gordon-Schrodinger equations, Sci. Chi. Math., 56(2013)915-932.[16] Wang S. and Zhang L., A class of conservative orthogonal spline collocation schemes forsolving coupled Klein-Gordon-Schrodinger equations, Appl. Math. Comput., 203 (2008)799-812.[17] Dehghan M. and Taleei A., Numerical solution of the Yukawa-coupled Klein-Gordon-Schrodinger equations via a Chebyshev pseudospectral multidomain method, Appl. Math.Model., 36 (2012) 2340-2349.[18] Zhang J. and Kong L., New energy-preserving schemes for Klein-Gordon-Schrodinger equations,Appl. Math. Model., 40 (2016) 6969-6982.[19] Zhang L., Convergence and stability of a conservative nite difference scheme for a classof equation system in interaction of complex Schrodinger eld and real Klein-Gordon eld,Numer. Math. A. J. Chinese. Univ., 22 (2000) 362-370.[20] Zhang L., Convergence of a conservative difference schemes for a class of Klein-Gordon-Schrodinger equations in one space dimension, Appl. Math. Comput., 163 (2005) 343-355.[21] Wang T. and Jiang Y., Point-wise errors of two conservative difference schemes for theKlein-Gordon-Schrodinger equation, Commun. Nonlinear Sci. Numer. Simul., 17 (2012)4565-4575.[22] Wang T. and Guo B., Unconditional convergence of two conservative compact dierenceschemes for non-linear Schrodinger equation in one dimension (in Chinese), Sci. Sin. Math.,41 (2011) 207-233.[23] Wang T., Guo B. and Xu Q., Fourth-order compact and energy conservative differenceschemes for the nonlinear Schrodinger equation in two dimensions, J. Comput. Phys., 243(2013) 382-399.[24] Pan X. and Zhang L., High-order linear compact conservative method for the nonlinearSchrodinger equation coupled with the nonlinear Klein-Gordon equation, Nonlinear Anal.,92 (2013) 108-118.[25] Sun Q., Zhang L., Wang S. and Hu X., A conservative compact difference scheme for thecoupled Klein-Gordon-Schrodinger equation. Numerical Methods for Partial DifferentialEquations, 29 (2013) 1657-1674.[26] Wang T., Optimal point-wise error estimate of a compact difference scheme for the Klein-Gordon-Schrodinger equation, J. Math. Anal. Appl., 412 (2014) 155-167.[27] Sun Z. and Zhu Q., On Tsertsvadzes difference scheme for the Kuramoto-Tsuzuki equation,J. Comput. Appl. Math., 98 (1998) 289-304.[28] Zhou Y., Application of Discrete Functional Analysis to the Finite Difference Method, Inter.Acad. Publishers, Beijing, 1990.[29] Xia J. and Wang M., Exact solitary solution of coupled Klein-Gordon-Schrodinger equations,Appl. Math. Mech., 23 (2002) 52-57.

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