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A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrodinger system

机译:基于隐式完全离散局部不连续Galerkin方法的时分耦合薛定inger系统的数值研究

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摘要

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrodinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L~2 error estimate has the convergence rate O(h~(k+1) + (△t)~2 + (△t)2/a h~(k+2/1)) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.
机译:在本文中,我们开发和分析了一种隐式全离散局部不连续伽勒金(LDG)有限元方法,用于求解时间分数耦合Schrodinger系统。该方法基于时间上的有限差分方案和空间中的局部不连续Galerkin方法。通过分析表明,该方案是无条件稳定的,L〜2误差估计具有收敛速度O(h〜(k + 1)+(△t)〜2 +(△t)2 / ah〜(k + 2/1))。提供大量的数值结果来证明该方案的效率和准确性。

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