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

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 $L_{\infty }$ L ∞ -norm. The convergence order is $O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$ O ( τ 2 − α + 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.