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Hu, Xiuling; Liu, Fawang; Turner, Ian; Anh, Vo

An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation. (English) Zbl 1343.65110

Numer. Algorithms 72, No. 2, 393-407 (2016).
The authors discuss an implicit numerical method of a new time distributed-order and two-sided space fractional advection-dispersion equation. Based on the observations from several papers in the literature, the authors focus on deriving a numerical method for a new time distributed-order and two-sided space fractional advection-dispersion equation (TDO-TSSFADE). An implicit numerical method is proposed for the TDO-TSSFADE. The uniqueness, stability and convergence of the implicit numerical method are discussed. Some numerical results are presented to illustrate the effectiveness of the method.
Reviewer: Seenith Sivasundaram (Daytona Beach)

Cited in 25 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35L20 Initial-boundary value problems for second-order hyperbolic equations

Keywords:

implicit numerical method; distributed-order fractional derivative; two-sided space-fractional derivative; stability; convergence; advection-dispersion equation; numerical result

Software:

ma2dfc
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Full Text: DOI Link

References:

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