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.

引用

页数：14

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