Non-polynomial spline method for the time-fractional nonlinear Schrodinger equation

被引：21
|
作者：
Li, Mingzhu [1 ,2 ]
Ding, Xiaohua [1 ]
Xu, Qiang [3 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin, Heilongjiang, Peoples R China
[2] Qingdao Univ Qingdao, Sch Sci, Qingdao, Peoples R China
[3] Shandong Normal Univ, Sch Math & Stat, Jinan, Shandong, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
关键词：
Fractional Schrodinger equation; Non-polynomial spline; Stability; Fourier analysis; SPECTRAL COLLOCATION APPROXIMATION; SUB-DIFFUSION EQUATIONS; SYSTEM;
D O I：
10.1186/s13662-018-1743-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 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(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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页数：15
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