STABILITY AND ERROR ANALYSIS FOR A SECOND-ORDER FAST APPROXIMATION OF THE ONE-DIMENSIONAL SCHRODINGER EQUATION UNDER ABSORBING BOUNDARY CONDITIONS

作     者：Li, Buyang Zhang, Jiwei Zheng, Chunxiong 

作者机构：Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Wuhan Univ Sch Math & Stat Hubei Key Lab Computat Sci Wuhan 430072 Hubei Peoples R China Tsinghua Univ Dept Math Sci Beijing Peoples R China 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：2018年第40卷第6期

页      面：A4083-A4104页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Research Grants Council of the Hong Kong Special Administrative Region NSFC [91630205, 11771248] NSAF [U1530401] 

主　　题：Schrodinger equation absorbing boundary condition fast algorithm Gaussian quadrature stability error estimate 

摘      要：A second-order Crank-Nicolson finite difference method, integrating a fast approximation of an exact discrete absorbing boundary condition, is proposed for solving the one-dimensional Schrodinger equation in the whole space. The fast approximation is based on Gaussian quadrature approximation of the convolution coefficients in the discrete absorbing boundary conditions. It approximates the time convolution in the discrete absorbing boundary conditions by a system of O(log(2) N) ordinary differential equations at each time step, where N denotes the total number of time steps. Stability and an error estimate are presented for the numerical solutions given by the proposed fast algorithm. Numerical experiments are provided, which agree with the theoretical results and show the performance of the proposed numerical method.