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Khodabandehloo, H., Shivanian, E., Mostafaee, S. (2018). The new Implicit Fi nite Difference Method for the Solution of Time Fractional Advection-Dispersion Equation. Theory of Approximation and Applications, 12(1), 65-76.
Hamid Reza Khodabandehloo; Elyas Shivanian; Sh. Mostafaee. "The new Implicit Fi nite Difference Method for the Solution of Time Fractional Advection-Dispersion Equation". Theory of Approximation and Applications, 12, 1, 2018, 65-76.
Khodabandehloo, H., Shivanian, E., Mostafaee, S. (2018). 'The new Implicit Fi nite Difference Method for the Solution of Time Fractional Advection-Dispersion Equation', Theory of Approximation and Applications, 12(1), pp. 65-76.
Khodabandehloo, H., Shivanian, E., Mostafaee, S. The new Implicit Fi nite Difference Method for the Solution of Time Fractional Advection-Dispersion Equation. Theory of Approximation and Applications, 2018; 12(1): 65-76.

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

Article 5, Volume 12, Issue 1, Winter and Spring 2018, Page 65-76  XML PDF (292.93 K)
Document Type: Research Articles
Authors
Hamid Reza Khodabandehloo orcid 1; Elyas Shivanian2; Sh. Mostafaee2
1Department of Mathematics, Payame Noor University (PNU),45771-13878, Qeydar, Zanjan, Iran
2Department 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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