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 L 1 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(τ 2-α + h 4) 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.

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The semidiscrete and fully discrete weak Galerkin finite element schemes for the linear parabolic integrodifferential equations are proposed. Optimal order error estimates are established for the corresponding numerical approximations in both L 2 and H 1 norms. Numerical experiments illustrating the error behaviors are provided.

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