TY - JOUR T1 - Optimal Error Estimates in Numerical Solution of Time Fractional Schrödinger Equations on Unbounded Domains 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 -
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.