Efficient Numerical Computation of Time-Fractional Nonlinear Schrodinger Equations in Unbounded Domain  

作　　者：Jiwei Zhang Dongfang Li Xavier Antoine 

机构地区：[1]Beijing Computational Science Research Center,Beijing 100193,P.R.China [2]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [3]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China [4]Institut Elie Cartan de Lorraine,UMR CNRS 7502,Universit́e de Lorraine,Inria Nancy-Grand Est,SPHINX Team,F-54506 Vandoeuvre-l`es-Nancy Cedex,France

出　　处：《Communications in Computational Physics》2019年第1期218-243,共26页计算物理通讯（英文）

基　　金：supported by the NSFC under grants 11771035,91430216,U1530401;supported by the NSFC under grants Nos.11571128,11771162;support of the French ANR grant BOND(ANR-13-BS01-0009-01)and the LIASFMA(funding from the University of Lorraine).

摘　　要：The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded domain.We first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization procedure.Then,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is stated.To accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional derivative.The resulting algorithm is highly efficient for long time simulations.Finally,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.

关 键 词：Time-fractional nonlinear Schrodinger equation absorbing boundary condition sta-bility analysis convergence analysis sum-of-exponentials approximation 

分 类 号：O17[理学—数学]