TY - JOUR
T1 - Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains
AU - Zhi-Zhong Sun, Jiwei Zhang & Zhimin Zhang
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 634
EP - 655
PY - 2018
DA - 2018/10
SN - 8
DO - http://doi.org/10.4208/eajam.190218.150718
UR - https://global-sci.org/intro/article_detail/eajam/12812.html
KW - Time fractional Schrödinger equation, artificial boundary method, optimal error estimate, stability and convergence.
AB - <p style="text-align: justify;">The artificial boundary method is used to reformulate the time fractional
Schrödinger equation on the real line as a bounded problem with exact artificial boundary
conditions. The problem appeared is solved by a numerical method employing the
L1-formula for the Caputo derivative and finite differences for spatial derivatives. The
convergence of the method studied and optimal error estimates in a special metric are
obtained. The technique developed here can be also applied to study the convergence
of approximation methods for standard Schrödinger equation.</p>