Solving the time - fractional schrodinger equation with the group preserving scheme

Abstract

In this paper a powerful numerical scheme is proposed to gain the numerical solutions of the time-fractional Schrodinger equation: i C Dα 0+,tw(x, t) + ϑ ∂ 2w(x,t) ∂x2 + δ|w(x, t)| 2w(x, t) + P(x, t)w(x, t) = F(x, t), 0 < α ≤ 1, ϑ and δ are real constants, p(x, t) is trapping potential. The time fractional C Dα 0+,tw is defined in Caputo definition. By using a fictitious ι we can convert the variable w(x, t) into a new variable by: (1 + ι) kw(x, t) = Ξ(x, t, ι), where 0 < k ≤ 1. In new space with a semi-discretization of w(x, t, ι) the group-preserving scheme is used to solve the problem.