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Su, Lijuan; Wang, Wenqia; Xu, Qiuyan

Finite difference methods for fractional dispersion equations. (English) Zbl 1193.65158

Appl. Math. Comput. 216, No. 11, 3329-3334 (2010).
Summary: The fractional weighted average finite difference method for space-fractional advection-dispersion equation is proposed, which is based on shifted Grünwald formula. This method is unconditionally stable, consistent and convergent. A numerical example is given, and the numerical results verify the theoretical conclusions.

Cited in 36 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

anomalous diffusion; fractional derivatives; space-fractional advection-dispersion equation; shifted Grünwald formula; stability; weighted average methods; stability; consistency; convergence; finite difference method; numerical example
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\textit{L. Su} et al., Appl. Math. Comput. 216, No. 11, 3329--3334 (2010; Zbl 1193.65158)
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References:

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