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 difference methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial differentialequations with variable coefficients on a nite domain. Stability, consistency, and (therefore) convergenceof the method are examined and the local truncation error is O(Δt + h). This study concernsboth theoretical and numerical aspects, where we deal with the construction and convergence analysisof the discretization schemes. The results are justied by some numerical implementations. Anumerical example with known exact solution is also presented, and the behavior of the error isexamined to verify the order of convergence.