Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions  

作　　者：Shengnan Kang Kenzu Abdella Macro Pollanen Shuhua Zhang Liang Wang 

机构地区：[1]Coordinated Innovation Center for Computable Modeling in Management Science,Tianjin University of Finance and Economics,Tianjin 300222,China [2]Department of Mathematics,Trent University,Peterborough,Ontario K9L 7B8,Canada [3]Coordinated Innovation Center for Computable Modeling in Management Science,Yango University,Fujian 350015,China

出　　处：《Advances in Applied Mathematics and Mechanics》2022年第6期1302-1332,共31页应用数学与力学进展（英文）

基　　金：the Natural Sciences and Engineering Research Council of Canada,and the National Natural Science Foundation of China(Nos.11771322,and 72071140).

摘　　要：This paper presents the numerical solution of the time-dependent Gross-Pitaevskii Equation describing the movement of quantum mechanics particles under non-homogeneous boundary conditions.Due to their inherent non-linearity,the equation generally can not be solved analytically.Instead,a highly accurate approximation to the solutions defined in a finite domain is proposed,using the Crank-Nicolson difference method and Sinc Collocation numerical methods to discretize separately in time and space.Two Sinc numerical approaches,involving the Sinc Collocation Method(SCM)and the Sinc Derivative Collocation Method(SDCM),are easy to implement.The results demonstrate that Sinc numerical methods are highly efficient and yield accurate results.Mainly,the SDCM decays errors faster than the SCM.Future work suggests that the SDCM can be extensively applied to approximate solutions under other boundary conditions to demonstrate its broad applicability further.

关 键 词：Quantum mechanics spectral method time-dependent partial differential equation boundary value problem. 

分 类 号：O17[理学—数学]