Affiliation:
1. College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Abstract
In this paper, we first established a high-accuracy difference scheme for the time-fractional Schrödinger equation (TFSE), where the factional term is described in the Caputo derivative. We used the L1-2-3 formula to approximate the Caputo derivative, and the fourth-order compact finite difference scheme is utilized for discretizing the spatial term. The unconditional stability and convergence of the scheme in the maximum norm are proved. Finally, we verified the theoretical result with a numerical test.
Funder
Natural Science Foundation of Xinjiang Uygur Autonomous
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis