The new implicit fi nite difference method for the solution of time fractional advection-dispersion equation

In this paper, a numerical solution of time fractional advection-dispersion equations are presented. The new implicit nite di erence methods for solving these equations are studied. We examine practical numerical methods to solve a class of initial-boundary value fractional partial di erential equations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergence of the method are examined and the local truncation error is O(Δt h). This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. The results are justi ed by some numerical implementations. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.