Numerical Computations of Nonlocal Schrodinger Equations on the Real Line  

作　　者：Yonggui Yan Jiwei Zhang Chunxiong Zheng 

机构地区：[1]Beijing Computational Science Research Center,Beijing 100093,China [2]School of Mathematics and Statistics,and Hubei Key Laboratory of Computational Science,Wuhan University,Wuhan 430072,China [3]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China [4]College of Mathematics and Systems Science,Xinjiang University,Unimqi 830046,China

出　　处：《Communications on Applied Mathematics and Computation》2020年第2期241-260,共20页应用数学与计算数学学报（英文）

基　　金：Jiwei Zhang is partially supported by the National Natural Science Foundation of China under Grant No.11771035;the NSAF U1530401;the Natural Science Foundation of Hubei Province No.2019CFA007;Xiangtan University 2018ICIP01;Chunxiong Zheng is partially supported by Natural Science Foundation of Xinjiang Autonom ous Region under No.2019D01C026;the National Natural Science Foundation of China under Grant Nos.11771248 and 91630205。

摘　　要：The numerical computation of nonlocal Schrödinger equations (SEs) on the whole real axis is considered. Based on the artifcial boundary method, we frst derive the exact artifcial nonrefecting boundary conditions. For the numerical implementation, we employ the quadrature scheme proposed in Tian and Du (SIAM J Numer Anal 51:3458-3482, 2013) to discretize the nonlocal operator, and apply the z-transform to the discrete nonlocal system in an exterior domain, and derive an exact solution expression for the discrete system. This solution expression is referred to our exact nonrefecting boundary condition and leads us to reformulate the original infnite discrete system into an equivalent fnite discrete system. Meanwhile, the trapezoidal quadrature rule is introduced to discretize the contour integral involved in exact boundary conditions. Numerical examples are fnally provided to demonstrate the efectiveness of our approach.

关 键 词：Nonrefecting boundary conditions Artifcial boundary method Nonlocal Schrödinger equation Z-TRANSFORM Nonlocal models 

分 类 号：O17[理学—数学]