The global analysis on the spectral collocation method for time fractional Schrödinger equation

In this paper, a spectral collocation method is proposed and analyzed for solving the time fractional Schrödinger equation. The space derivative is discretized using the collocation method and the time fractional derivative using Grünwald–Letnikov formulation. The stability and convergence of the full discretization scheme are analyzed based on the z-transform. The global behavior of the finite difference spectral collocation method is derived. Numerical examples show a good agreement with the theoretical analysis.</p