Optimal error analysis of the Alikhanov formula for a time-fractional Schrodinger equation

被引：7
|
作者：
Zhao, Guoye [1 ]
An, Na [1 ]
Huang, Chaobao [2 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2023年 / 69卷 / 01期
基金：
中国国家自然科学基金;
关键词：
lime-fractional Schrodinger equations; The Alikhanov formula; Finite element methods; Graded meshes; Weak singularity; SCHEMES;
D O I：
10.1007/s12190-022-01733-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we have developed a fully discrete Alikhanov finite element method to solve the time-fractional Schrodinger equation with non-smooth solution. The proposed scheme uses the Alikhanov formula on graded meshes to approximate the Caputo fractional derivative in temporal direction and the standard finite element method in spatial direction. Furthermore, the L-2(Omega)-norm stability and the optimal convergent result for the computed solution are derived. Finally, a numerical example is presented to verify the accuracy of the proposed scheme.
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页码：159 / 170
页数：12
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