Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain

The aim of this paper is to derive an efficient scheme for solving one-dimensional time-fractional nonlinear Schrodinger equations set in unbounded domains. We first derive some absorbing boundary conditions for the fractional system by using the unified approach introduced in [57,58] and a linearization procedure. Then, the initial boundary-value problem for the fractional system with ABCs is discretized and the error estimate O(h 2 + τ) is stated. To accelerate the scheme in time, the fractional derivative is approximated through a linearized L1-scheme. Finally, we end the paper by some numerical simulations to validate the properties (accuracy and efficiency) of the derived scheme. In addition, we illustrate the behavior of the solution by reporting a few simulations for various parameter values of the fractional order 0 < α < 1, nonlinearities and potentials.

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