Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation

In this paper, we propose a cubic non-polynomial spline method to solve the time-fractional nonlinear Schrödinger equation. The method is based on applying the L₁ formula to approximate the Caputo fractional derivative and employing the cubic non-polynomial spline functions to approximate the spatial derivative. By considering suitable relevant parameters, the scheme of order O(τ2-α+h⁴) has been obtained. The unconditional stability of the method is analyzed by the Fourier analysis. Numerical experiments are given to illustrate the effectiveness and accuracy of the proposed method.