A Predictor-Corrector Compact Difference Scheme for a Nonlinear Fractional Differential Equation

被引：39
|
作者：
Jiang, Xiaoxuan [1 ]
Wang, Jiawei [1 ]
Wang, Wan [1 ]
Zhang, Haixiang [1 ]
机构：
[1] Hunan Univ Technol, Coll Sci, Zhuzhou 412008, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 07期
基金：
中国国家自然科学基金;
关键词：
nonlinear fractional differential equation; compact difference; predictor-corrector method; existence and uniqueness; TIME 2-GRID ALGORITHM; BURGERS-EQUATION;
D O I：
10.3390/fractalfract7070521
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, a predictor-corrector compact difference scheme for a nonlinear fractional differential equation is presented. The MacCormack method is provided to deal with nonlinear terms, the Riemann-Liouville (R-L) fractional integral term is treated by means of the second-order convolution quadrature formula, and the Caputo derivative term is discretized by the L1 discrete formula. Through the first and second derivatives of the matrix under the compact difference, we improve the precision of this scheme. Then, the existence and uniqueness are proved, and the numerical experiments are presented.
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收藏
页数：13
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