The new Implicit Fi nite Difference Method for the Solution of Time Fractional Advection-Dispersion Equation

Document Type: Research Articles

Authors

1 Department of Mathematics, Payame Noor University (PNU),45771-13878, Qeydar, Zanjan, Iran

2 Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

Abstract

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 examine
practical numerical methods to solve a class of initial-boundary value fractional partial differential
equations with variable coefficients 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.

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