TITLE:
A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation
AUTHORS:
Baojin Su, Yanan Wang, Jingwen Qi, Yousen Li
KEYWORDS:
Multi-Term Time Fractional Sub-Diffusion Equation, High-Order Compact Finite Volume Scheme, Stable, Convergent
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.10,
October
27,
2022
ABSTRACT: 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(τ2-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.