时空分数阶薛定谔方程的指数时间差分方法

梁霄, Harish BHATT

数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 663-672.

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数学学报 ›› 2019, Vol. 62 ›› Issue (4) : 663-672. DOI: 10.12386/A2019sxxb0062
论文

时空分数阶薛定谔方程的指数时间差分方法

    梁霄1, Harish BHATT2
作者信息 +

Exponential Time Differencing Methods for the Time-Space-Fractional Schrödinger Equation

    Xiao LIANG1, Harish BHATT2
Author information +
文章历史 +

摘要

本文针对时空分数阶非线性薛定谔方程,提出了应用Padé,近似逼近Mittag-Leffler函数的指数时间差分格式,讨论了提高格式计算效率的方法.本文在具有各种参数的时空分数阶非线性薛定谔方程上进行了数值实验,实验结果说明了所提出方法的准确性、有效性和可靠性.

Abstract

In this paper, exponential time differencing schemes with Padé approximation to the Mittag-Leffler function are proposed for the time-space-fractional nonlinear Schrödinger equation. Ways of increasing the efficiency of the proposed schemes are discussed. Numerical experiments are performed on the time-space-fractional nonlinear Schrödinger equations with various parameters. The accuracy, efficiency, and reliability of the proposed method are illustrated by numerical results.

关键词

分数阶非线性薛定谔方程 / 指数时间差分 / Padé / 近似 / 时空分数阶

Key words

fractional nonlinear Schrödinger equations / exponential time differencing / Padé / approximation / time-space-fractional

引用本文

导出引用
梁霄, Harish BHATT. 时空分数阶薛定谔方程的指数时间差分方法. 数学学报, 2019, 62(4): 663-672 https://doi.org/10.12386/A2019sxxb0062
Xiao LIANG, Harish BHATT. Exponential Time Differencing Methods for the Time-Space-Fractional Schrödinger Equation. Acta Mathematica Sinica, Chinese Series, 2019, 62(4): 663-672 https://doi.org/10.12386/A2019sxxb0062

参考文献

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基金

湖北省教育厅指导性项目(B2018158);湖北文理学院开放基金项目(XK2018033)

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