A Temporal Second-Order Difference Scheme for Variable-Order-Time Fractional-Sub-Diffusion Equations of the Fourth Order

被引：0
作者：
Zhang, Xin [1 ]
Bo, Yu [2 ]
Jin, Yuanfeng [1 ,2 ]
机构：
[1] Harbin Engn Univ, Dept Math Sci, Harbin 150001, Peoples R China
[2] Yanbian Univ, Dept Math, Yanji 133002, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 02期
关键词：
variable-order-time fractional-sub-diffusion equation of the fourth-order; compact finite difference scheme; solvable; stability; convergence; NUMERICAL-METHODS; DISCRETIZATION; MODELS;
D O I：
10.3390/fractalfract8020112
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we develop a compact finite difference scheme for a variable-order-time fractional-sub-diffusion equation of a fourth-order derivative term via order reduction. The proposed scheme exhibits fourth-order convergence in space and second-order convergence in time. Additionally, we provide a detailed proof for the existence and uniqueness, as well as the stability of scheme, along with a priori error estimates. Finally, we validate our theoretical results through various numerical computations.
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页数：14
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