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

Abstract

AbstractBased on anL1 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(τ2−α+h14+h24), whereτis the temporal step size and$h_{1}$h1is the spatial step size in one direction,$h_{2}$h2is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.