Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation
2018
In this paper, we propose a cubic non-polynomial spline method to solve the time-fractional nonlinear Schrodinger equation. The method is based on applying the L
1
$L_{1}$
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
)
$O(\tau^{2-\alpha }+h^{4})$
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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