A Family of Transformed Difference Schemes for Nonlinear Time-Fractional Equations

被引：3
作者：
Qin, Hongyu [1 ]
Chen, Xiaoli [2 ,3 ]
Zhou, Boya [4 ]
机构：
[1] Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China
[2] Natl Univ Singapore, Inst Funct Intelligent Mat, Singapore 117544, Singapore
[3] Natl Univ Singapore, Dept Math, Singapore 119077, Singapore
[4] Foshan Univ, Sch Math & Big Data, Foshan 528000, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 01期
基金：
中国国家自然科学基金;
关键词：
time-fractional parabolic problems; change in variable; convergence; optimal error estimates; linearized schemes; CONVOLUTION QUADRATURE; NUMERICAL-METHODS;
D O I：
10.3390/fractalfract7010096
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we present a class of finite difference methods for numerically solving fractional differential equations. Such numerical schemes are developed based on the change in variable and piecewise interpolations. Error analysis of the numerical schemes is obtained by using a Gronwall-type inequality. Numerical examples are given to confirm the theoretical results.
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页数：11
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