Compact finite difference scheme for the solution of time fractional advection-dispersion equation

摘要

In this paper, a compact finite difference method is proposed for the solution of time fractional advection-dispersion equation which appears extensively in fluid dynamics. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ 2 − α ), 0 < α < 1, and spatial derivatives are replaced with a fourth order compact finite difference scheme. We will prove the unconditional stability and solvability of proposed scheme. Also we show that the method is convergence with convergence order O(τ 2 − α  + h 4). Numerical examples confirm the theoretical results and high accuracy of proposed scheme.