7fe56d46-480b-4fbf-818a-037614654af120220308062550286naun:naunmdt@crossref.orgMDT DepositInternational Journal of Computers and Communications2074-129410.46300/91013http://www.naun.org/cms.action?id=30503820223820221610.46300/91013.2022.16https://npublications.com/journals/cc/2022.phpMorenoConcezziDepartment of Mathematics and Physics, University “Roma Tre”, Rome, ItalyRenatoSpiglerDepartment of Mathematics and Physics, University “Roma Tre”, Rome, ItalyADI methods can be generalized to solve numerically multidimensional fractional diffusion equations, which describe fluid flows through porous media better than classical diffusion equations. A new, unconditionally stable, second-order and well balanced in space, third-order in time ADI scheme has been constructed and its convergence accelerated by an extrapolation technique coupled with the PageRank algorithm.3820223820229122https://npublications.com/journals/cc/2022/a042012-002(2022).pdf10.46300/91013.2022.16.2https://npublications.com/journals/cc/2022/a042012-002(2022).pdf10.1007/s12190-007-0013-4Chen, S.,Liu, F., ADI-Euler and extrapolation methods for the two dimensional fractional advection-dispersion equation, J. Appl. Math. Comp., 26, 295-311, 2008. Chou, H., Lee, B., and Chen, C, The transient infiltration process for seepage flow from cracks, Western Pacific Meeting, Advances in Subsurface Flow and Transport: Eastern and Western Approaches III, Eos Trans. AGU, 2006. 10.3390/fractalfract4040057Concezzi, M., Spigler, R., Numerical solution of two-dimensional fractional diffusion equations by a high-order ADI method, Commun. Appl. Ind. Math., 2013, printed online; 3, No. 2 (2012), in print. [http://dx.doi.org/10.1685/journal.caim.421] 10.3390/fractalfract4040057Concezzi, M., Spigler, R., An ADI method for the numerical solution of 3D fractional reaction-diffusion equations in porous media, 2014, submitted. Darcy, H., Les fontaines publique de la Ville de Dijon, Western Paris, France: Dalmont, 1856. Deng, W., Chen, M., Efficient numerical algorithms for three-dimensional fractional partial differential equations, arXiv:1303.4628v1, 2013. 10.1016/s0045-7825(98)00108-xHe, J., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. 167, 57-68, 1998. 10.1145/775152.775190Kamvar, S., Haveliwala, T., Manning, C., and Golub, G., Extrapolation Methods for Accelerating PageRank Computations, Welfth International World Wide Web Conference, 2003. 10.21914/anziamj.v45i0.901Liu, F., Anh, V., Turner, I., Zhunag, P.Numerical simulation for solute transport in fractal porous media, ANZIAM J. 45, 461-473., 2004. 10.1093/imamat/hxn044Liu, Q., Liu, F., Turner, I., and Anh, V., Numerical simulation for the 3D seepage flow with fractional derivatives in porous media, IMA J. Appl. Math. 74 , 178-200, 2009. 10.1016/s1001-6058(08)60100-6Luo, Z.-J., Zhang, Y.-Y., and Wu, Y.-X., Finite element numerical simulation of three-dimensional seepage control for deep foundation pit dewatering, Hydrodyn. 20, 596-602, 2008. Marchuk, G.I., and Shaidurov, V.V., Difference Methods and Their Extrapolations, Springer-Verlag, New York, 1983. 10.1016/j.cam.2004.01.033Meerschaert, M. M. and Tadjeran, C., Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172, 65-77. 2004. Podlubny, I., Fractional Differential Equations, New York: Academic Press, 1999. Roop, J. P., Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R2 , J. Comput. Appl. Math. 193, 243-268, 2006. Rushton, K. R. and Redshaw, S. C, Seepage and Groundwater Flow, Brisbane, Australia: Wiley-Interscience Publication, 1979. 10.21914/anziamj.v46i0.995Shen, S. and Liu, F., Error analysis of an explicit finite difference approximation for the space fractional diffusion with insulated ends, ANZIAM J. 46, 871-887, 2005. Smith, D.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford Applied Mathematics and Computing Sciences Series, Oxford University Press, 1990. 10.1002/nme.2165Yu, Q., Liu, F., Anh, V., and Turner, I., Solving linear and nonlinear space-time fractional reaction-diffusion equations by Adomian decomposition method, Int. J. Numer. Methods Eng. 74, 138-158., 2008.