Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation

Abstract

Abstract In this paper, we shall solve a time-fractional nonlinear Schrödinger equation by using the quintic non-polynomial spline and the L 1 formula. The unconditional stability, unique solvability and convergence of our numerical scheme are proved by the Fourier method. It is shown that our method is sixth order accurate in the spatial dimension and $(2-\gamma )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>−</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo></mml:math> th order accurate in the temporal dimension, where γ is the fractional order. The efficiency of the proposed numerical scheme is further illustrated by numerical experiments, meanwhile the simulation results indicate better performance over previous work in the literature.