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 di erence methods for solving these equations are studied. We examine practical numerical methods to solve a class of initial-boundary value fractional partial di erential equations with variable coecients 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.
Article Title [Persian]
The new implicit fi nite difference method for the solution of time fractional
advection-dispersion equation
References
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