High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

Abstract

Abstract Based on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable in L ∞ $L_{\infty }$ -norm. The convergence order is O ( τ 2 − α + h 1 4 + h 2 4 ) $O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$ , where τ is the temporal step size and h 1 $h_{1}$ is the spatial step size in one direction, h 2 $h_{2}$ is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

Keywords

• 2D multi-term time fractional sub-diffusion equation
• High-order compact finite volume scheme
• Stable
• Convergent