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一种求解与时间有关的二维薛定谔方程的数值算法 被引量：1

A Numerical Method for Solving Two-dimensional Time-dependent Schrdinger Equation
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摘要 在有限差分和径向基函数的基础上,利用无网格法中的特解方法来给出与时间有关的二维薛定谔方程的一种数值算法,同时给出了两个例子来说明这种方法良好的准确性,并取得了比较好的数值结果. Based on the finite difference scheme and radial basis functions,this paper gives a new numerical scheme using one of the meshless method which is called the method of particular solutions for solving twodimensional time-dependent schrdinger equation.Two numerical examples with good accuracy are given to validate the proposed method.
作者 王国栋 姜同松
机构地区 曲阜师范大学运筹与管理学院 临沂师范学院理学院
出处 《临沂师范学院学报》 2010年第6期1-7,共7页 Journal of Linyi Teachers' College
基金 国家自然科学基金项目(10671086) 山东省自然科学基金项目(ZR2010AM014)资助
关键词 薛定谔方程 有限差分 径向基函数 无网格法 数值解 Schrdinger equation finite difference radial basis functions numerical solution
分类号 O241.82 [理学—计算数学]
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参考文献11

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同被引文献14

  • 1M.A.Golberg A.S.Muleshkov and C.S.Chen.Particular solutions of helmholtz-type operators using higher order polyharmonic splines.Comput.Mechanics,24:411-419,1999.
  • 2X.Antoine and C.Besse. Unconditionally stablediscretization schemes of non-reecting boundary conditions for the one-dimensional dinger equation.J.Comput.Phys., 188: 157-75,2003.
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  • 5C.S.Chen, C.M Fan,and P.H.Wen.The method of particular solutions for solving elliptic problems with variable coeffcients.to appear in Communica- tion in Numerical Methods in Engineering.
  • 6W.Chen.Symmetric boundary knot method.Engineering Analysis with Boundary Elements,26:489-494,2002.
  • 7A.H.D.Cheng.Particular solutions of laplacian,helmholtz-type,and polyharmonic operators involving higher order radial basis functions.Eng.Analy.Boundary Elements,24:531-538,2000.
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  • 10H.Han,J.Jin,and X.Wu.A finite difference method for the one-dimentional time-dependent dinger equation on unbounded domain.Comput.Math.Appl.,50:1345-362,2005.

引证文献1

临沂师范学院学报
2010年 第6期

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