An Efficient Numerical Scheme for Variable-Order Fractional Sub-Diffusion Equation

被引：18

作者：

Ali, Umair ^{[1
,2
]}

Sohail, Muhammad ^{[3
]}

Abdullah, Farah Aini ^{[2
]}

机构：

[1] AL Fajar Univ, Dept Math, Mari Indus 42350, Pakistan

[2] Univ Sains Malaysia, Sch Math Sci, Usm Penang 11800, Malaysia

[3] Inst Space Technol, Dept Appl Math & Stat, Islamabad 44000, Pakistan

来源：

SYMMETRY-BASEL | 2020年 / 12卷 / 09期

关键词：

variable-order fractional sub-diffusion equation; implicit difference method; stability; consistency; convergence; DIFFERENCE SCHEME; SPATIAL ACCURACY;

D O I：

10.3390/sym12091437

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The variable-order (VO) fractional calculus can be seen as a natural extension of the constant-order, which can be utilized in physical and biological applications. In this study, we derive a new numerical approximation for the VO fractional Riemann-Liouville integral formula and developed an implicit difference scheme (IDS) for the variable-order fractional sub-diffusion equation (VO-FSDE). The derived approximation used in the VO time fractional derivative with the central difference approximation for the space derivative. Investigated the unconditional stability by the van Neumann method, consistency, and convergence analysis of the proposed scheme. Finally, a numerical example is presented to verify the theoretical analysis and effectiveness of the proposed scheme.

引用

页数：12

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