期刊文献+

一类非线性Schrdinger方程的数值解

Numerical approximation of solution for a class of nonlinear Schrdinger equation
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摘要 对一类带五次项的非线性Schrdinger方程的初边值问题提出一个新的守恒差分格式,并在先验估计的基础上证明了格式的稳定性和收敛性,数值实验结果表明此格式是有效可靠的. In this work, a new conservative difference scheme is presented for the initial-boundary value problem of the class of nonlinear Schrodinger equation involving quintic term. On the basis of a priori estimates, convergence and stability of the numerical solution are proved. Numerical experi- ments demonstrate the accuracy and effectiveness of the proposed scheme.
作者 陈娟 凡震彬
出处 《扬州大学学报(自然科学版)》 CAS CSCD 北大核心 2012年第3期27-29,41,共4页 Journal of Yangzhou University:Natural Science Edition
基金 国家自然科学基金资助项目(11001034)
关键词 Schrdinger方程 守恒差分格式 先验估计 收敛性 Schrodinger equation conservative difference scheme priori estimates convergence
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参考文献16

  • 1MENYUK C R. Stability of solitons in birefringent optical fibers:II. arbitrary amplitudes [J]. J Opt Soc Amer B: Opt Phys, 1988, 5(2): 392-402. 被引量:1
  • 2WANG Ting-chun, NIE Tao, ZHANG I.u-ming, et al. Numerical simulation of a nonlinearly coupled SehrOdinger system: a linearly uncoupled finite difference scheme[J]. Math & Comput in Simulation, 2008, 79(3) : 607-621. 被引量:1
  • 3ZISOWSKY A, EHRHARDT M. Discrete artificial boundary conditions for nonlinear Schr6dinger equations [J]. Math Comput Modelling, 2008, 47(11/12): 1264-1283. 被引量:1
  • 4SUN Zhi-zhong, ZHAO Dan-dan. On the L∞ convergence of a difference scheme for coupled nonlinear Schrodinger equations [J]. Comput Math Appl, 2010, 59(10) :3286-3300. 被引量:1
  • 5WANG Ting-chun, GUO Bo-ling. Unconditional convergenee of two conservative compact difference schemes for non-linear Schr6dinger equation in one dimension[J]. Sci Sin Math,2011, 41(3): 207-233. 被引量:1
  • 6ISMAIL M S. Numerical solution of coupled nonlinear Schr/3dinger equation by Galerkin method [J]. Math Com- put in Simulation, 2008, 78(4): 532-547. 被引量:1
  • 7ZLOTNIK A, DUCOMET B, GOUTTE H, et al. On one semidiscrete Galerkin method for a generalized time dependent 2D Schr0dinger equation [J]. Appl Math Lett, 2009, 22(2): 252-257. 被引量:1
  • 8MATSUO T. Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution euations [J]. J Comput Appl Math, 2008, 218(2):506-521. 被引量:1
  • 9JIN Ji-cheng, WU Xiao-nan. Analysis of finite element method for one dimensional time-dependent Schrosdinger equation on unbounded domain [J]. J Comput Appl Math, 2008, 220(1/2) : 240-256. 被引量:1
  • 10JIN Ji-cheng, WU Xiao-nan. Convergence of a finite element scheme for the two-dimensional time-dependent Schrodinger equation in along strip [J]. J Comput Appl Math, 2010, 234(3): 777-793. 被引量:1

二级参考文献24

  • 1CRANK J. Free and moving boundary problems [M]. Oxford: Clarendon Press, 198,1: 1-23. 被引量:1
  • 2OCKENDON J R, HODGKINS W R. Moving boundary problems in heat flow anti diffusion [M]. Oxford: Clarendon Press, 1975: 1-20. 被引量:1
  • 3FRIEDMAN A, HU B. Asymptotic stability for a free boundary problem arising in a tumor model [J]. J Differ Eels, 2006, 227(2): 598-639. 被引量:1
  • 4TAO You-shan, CHEN Miao-jun. An elliptic-hyperbolic free boundary problem modelling cancer therapy [J].Nonlinearity, 2006, 19(2): 419-410. 被引量:1
  • 5AMADORI A L, VAZQUEZ J L. Singular free boundary prohlem from image processing[J]. Math Models Methods Appl Sci, 2005, 15(5): 689-715. 被引量:1
  • 6LIN Zhi-gui. A free boundary problem for a predator-prey model [J].Nonlinearity, 2007, 20(8): 1883-1892. 被引量:1
  • 7AZIZ A, NA T Y. Perturbation methods in heat transfer [M]. Washington: Hemisphere, 198,1: 21-49. 被引量:1
  • 8SPALL R.Spectral collocation methods for one dimensional phase change problems[J].Hear Mass Transfer. 38(15): 2713-2718. 被引量:1
  • 9ASAITHAMBI A. Numerical solution of Stefan problems using automatic differentiation [J].Appl Math Comput, 2007, 189(1 ) : 913-918. 被引量:1
  • 10FASANO A, PRIMICERIO M. Free boundary prohlems for nonlinear parabolic equations with nonlinear free boundary conditions [J]. J Math Anal Appl, 1979, 72(1): 247-273. 被引量:1

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