Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Schrödinger Equations (Journal of Computational Mathematics, 2023)
We present Alikhanov linearized Galerkin methods for solving the nonlinear time fractional Schr\u00f6dinger equations. Unconditionally optimal estimates of the fully-discrete scheme are obtained by using the fractional time-spatial splitting argument. The convergenceresults indicate that the error estimates hold without any spatial-temporal stepsize restrictions. Numerical experiments are done to verify the theoretical results.
Keywords: Fractional Grönwall type inequality; Nonlinear time-fractional Schrödinger equation; Error analysis.