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
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.
References
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