The new implicit finite 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 finite difference methods for solving these equations are studied. We examine practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined and the local truncation error is O(∆t + 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 justified 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.