Abstract
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.
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Mohebbi, A., Abbaszadeh, M. Compact finite difference scheme for the solution of time fractional advection-dispersion equation. Numer Algor 63, 431–452 (2013). https://doi.org/10.1007/s11075-012-9631-5
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DOI: https://doi.org/10.1007/s11075-012-9631-5