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Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schroedinger equation

机译:阻尼非线性分数次Schroedinger方程保守方案的最大范数误差分析

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This paper aims to construct a numerical scheme for the damped nonlinear space fractional Schrodinger equation. First, the conservation laws of mass and energy for the continuous equation are derived. Then, based on the fractional centered difference formula, a semi-discrete scheme, which preserves the semi-discrete mass and energy conservation laws is proposed. Further applying the Crank-Nicolson method on the temporal direction gives a fully-discrete conservative scheme. Furthermore, the solvability, boundedness and convergence in the maximum norm of the numerical solutions are given. Some numerical examples are displayed to confirm the theoretical results. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
机译:本文旨在为阻尼非线性空间分数薛定inger方程建立一个数值格式。首先,推导了连续方程的质量和能量守恒定律。然后,基于分数中心差公式,提出了一种保留半离散质量和能量守恒定律的半离散方案。在时间方向上进一步应用Crank-Nicolson方法可得到完全离散的保守方案。此外,给出了数值解的最大范数的可解性,有界性和收敛性。显示一些数值示例以确认理论结果。 (C)2019国际模拟数学与计算机协会(IMACS)。由Elsevier B.V.发布。保留所有权利。

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