2018 **Abstract:** According to the principle of conservation of mass and the fractional Fick's law, a new two-sided space-fractional diffusion equation was obtained. In this paper, we present two accurate and efficient numerical methods to solve this equation. First we discuss the alternating-direction finite difference method with an implicit Euler method (ADI-implicit Euler method) to obtain an unconditionally stable first-order accurate finite difference method. Second, the other numerical method combines the ADI with a Cran…

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“…There are numerical schemes that used to solve two-dimension space fractional diffusion problems such as the alternating direction implicit (ADI) method [25][26][27][28][29][30], the Galerkin finite element method [31], the finite volume method [32] and the kronecker product splitting method [33]. ADI and CN-ADI spectral methods are used to solve two-dimensional Riesz space fractional diffusion equation with a non-linear reaction term with respect to their error estimates have been discussed (see References [34,35]).…”

confidence: 99%

“…There are numerical schemes that used to solve two-dimension space fractional diffusion problems such as the alternating direction implicit (ADI) method [25][26][27][28][29][30], the Galerkin finite element method [31], the finite volume method [32] and the kronecker product splitting method [33]. ADI and CN-ADI spectral methods are used to solve two-dimensional Riesz space fractional diffusion equation with a non-linear reaction term with respect to their error estimates have been discussed (see References [34,35]).…”

confidence: 99%

“…In multidimensional case, lowering of computational complexity is often achieved using splitting schemes (Chen and Li 2016;Yin et al 2018;Samarskii 2001;Bogaenko et al 2017) that reduce multidimensional problems to the series of one-dimensional ones. In addition to the direct effect of complexity reduction, significant reduction in the connectivity between computation blocks makes it possible to apply parallelization techniques efficiently in this case.…”

confidence: 99%