TY - JOUR
T1 - Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain
AU - Jiwei Zhang, Dongfang Li & Xavier Antoine
JO - Communications in Computational Physics
VL - 1
SP - 218
EP - 243
PY - 2018
DA - 2018/09
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0195
UR - https://global-sci.org/intro/article_detail/cicp/12669.html
KW - Time-fractional nonlinear Schrödinger equation, absorbing boundary condition, stability analysis, convergence analysis, sum-of-exponentials approximation.
AB - <p style="text-align: justify;">The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrödinger 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<sup style="white-space: normal;">2</sup>+τ) is stated. To accelerate 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.</p>