Author(s)

Baojin Su¹, Yanan Wang¹, Jingwen Qi¹, Yousen Li^2*

¹Qihe County Yongfeng Experimental School, Dezhou, China.
²Middle School Affiliated to Shandong University, Jinan, China.

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.

Multi-Term Time Fractional Sub-Diffusion Equation, High-Order Compact Finite Volume Scheme, Stable, Convergent

Su, B. , Wang, Y. , Qi, J. and Li, Y. (2022) A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation. Journal of Applied Mathematics and Physics, 10, 3156-3174. doi: 10.4236/jamp.2022.1010210.