A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation  

作　　者：Baojin Su Yanan Wang Jingwen Qi Yousen Li Baojin Su;Yanan Wang;Jingwen Qi;Yousen Li(Qihe County Yongfeng Experimental School, Dezhou, China;Middle School Affiliated to Shandong University, Jinan, China)

机构地区：[1]Qihe County Yongfeng Experimental School, Dezhou, China [2]Middle School Affiliated to Shandong University, Jinan, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第10期3156-3174,共19页应用数学与应用物理（英文）

摘　　要：In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L_∞-norm. The convergence order is O(τ^2-α + h⁴). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L_∞-norm. The convergence order is O(τ^2-α + h⁴). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.

关 键 词：Multi-Term Time Fractional Sub-Diffusion Equation High-Order Compact Finite Volume Scheme Stable CONVERGENT 

分 类 号：O17[理学—数学]