{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T17:37:23Z","timestamp":1777397843924,"version":"3.51.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,8,29]],"date-time":"2012-08-29T00:00:00Z","timestamp":1346198400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2013,7]]},"DOI":"10.1007\/s11075-012-9631-5","type":"journal-article","created":{"date-parts":[[2012,8,28]],"date-time":"2012-08-28T06:21:59Z","timestamp":1346134919000},"page":"431-452","source":"Crossref","is-referenced-by-count":60,"title":["Compact finite difference scheme for the solution of time fractional advection-dispersion equation"],"prefix":"10.1007","volume":"63","author":[{"given":"Akbar","family":"Mohebbi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Abbaszadeh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,8,29]]},"reference":[{"key":"9631_CR1","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.amc.2007.09.020","volume":"198","author":"CM Chen","year":"2008","unstructured":"Chen, C.M., Liu, F., Burrage, K.: Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation. Appl. Math. Comput. 198, 754\u2013769 (2008)","journal-title":"Appl. Math. Comput."},{"key":"9631_CR2","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1016\/j.camwa.2011.03.065","volume":"62","author":"CM Chen","year":"2011","unstructured":"Chen, C.M., Liu, F., Turner, I., Anh, V.: Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes first problem for a heated generalized second grade fluid. Comput. Math. Appl. 62, 971\u2013986 (2011)","journal-title":"Comput. Math. Appl."},{"key":"9631_CR3","doi-asserted-by":"crossref","first-page":"5729","DOI":"10.1016\/j.amc.2010.12.049","volume":"217","author":"CM Chen","year":"2011","unstructured":"Chen, C.M., Liu, F., Turner, I., Anh, V.: Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term. Appl. Math. Comput. 217, 5729\u20135742 (2011)","journal-title":"Appl. Math. Comput."},{"key":"9631_CR4","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.apm.2007.11.005","volume":"33","author":"S Chen","year":"2009","unstructured":"Chen, S., Liu, F., Zhuang, P., Anh, V.: Finite difference approximations for the fractional Fokker\u2013Planck equation. Appl. Math. Model. 33, 256\u2013273 (2009)","journal-title":"Appl. Math. Model."},{"key":"9631_CR5","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s12190-007-0013-4","volume":"26","author":"S Chen","year":"2008","unstructured":"Chen, S., Liu, F.: ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation. J. Appl. Math. Comput. 26, 295\u2013311 (2008)","journal-title":"J. Appl. Math. Comput."},{"key":"9631_CR6","doi-asserted-by":"crossref","first-page":"7792","DOI":"10.1016\/j.jcp.2009.07.021","volume":"228","author":"M Cui","year":"2009","unstructured":"Cui, M.: Compact finite differnce method for the fractional diffusion equation. J. Comput. Phys. 228, 7792\u20137804 (2009)","journal-title":"J. Comput. Phys."},{"key":"9631_CR7","first-page":"21","volume":"7","author":"L Debnath","year":"2004","unstructured":"Debnath, L., Bhatta, D.: Solution to few liner fractional inhomogeneous partial differential equations in fluid mechanics. Frac. Calc. Appl. Anal. 7, 21\u201336 (2004)","journal-title":"Frac. Calc. Appl. Anal."},{"key":"9631_CR8","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1016\/j.matcom.2008.04.015","volume":"79","author":"M Dehghan","year":"2008","unstructured":"Dehghan, M., Mohebbi, A.: High-order compact boundary value method for the solution of unsteady convection-diffusion problems. Math. Comput. Simul. 79, 683\u2013699 (2008)","journal-title":"Math. Comput. Simul."},{"key":"9631_CR9","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.camwa.2004.10.003","volume":"48","author":"GJ Fix","year":"2004","unstructured":"Fix, G.J., Roop, J.P.: Least squares element solution of a fractional order two-point boundary value problem. Comput. Math. Appl. 48, 1017\u20131033 (2004)","journal-title":"Comput. Math. Appl."},{"key":"9631_CR10","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.amc.2006.08.162","volume":"191","author":"F Liu","year":"2007","unstructured":"Liu, F., Zhuang, P., Anh, V., Turner, I., Burrage, K.: Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Appl. Math. Comput. 191, 12\u201320 (2007)","journal-title":"Appl. Math. Comput."},{"key":"9631_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00466-011-0573-x","volume":"48","author":"Q Liu","year":"2011","unstructured":"Liu, Q., Gu, Y., Zhuang, P., Liu, F., Nie, Y.: An implicit RBF meshless approach for time fractional diffusion equations. Comput. Mech. 48, 1\u201312 (2011)","journal-title":"Comput. Mech."},{"key":"9631_CR12","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"KS Miller","year":"1974","unstructured":"Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. New\u00a0York and London, Academic Press (1974)"},{"key":"9631_CR13","doi-asserted-by":"crossref","first-page":"3071","DOI":"10.1016\/j.apm.2010.01.013","volume":"34","author":"A Mohebbi","year":"2010","unstructured":"Mohebbi, A., Dehghan, M.: High-order compact solution of the one-dimensional heat and advection-diffusion equation. Appl. Math. Model. 34, 3071\u20133084 (2010)","journal-title":"Appl. Math. Model."},{"key":"9631_CR14","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1002\/num.20324","volume":"24","author":"S Momani","year":"2008","unstructured":"Momani, S., Odibat, Z.: Numerical solutions of the space-time fractional advection-dispersion equation. Numer. Methods Partial Differ. Equ. 24, 1416\u20131429 (2008)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"9631_CR15","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1016\/j.camwa.2008.02.015","volume":"56","author":"DA Murio","year":"2008","unstructured":"Murio, D.A.: Implicit finite difference approximation for time fractional diffusion equations. Comput. Math. Appl. 56, 1138\u20131145 (2008)","journal-title":"Comput. Math. Appl."},{"key":"9631_CR16","doi-asserted-by":"crossref","first-page":"2199","DOI":"10.1016\/j.camwa.2009.03.009","volume":"58","author":"Z Odibat","year":"2009","unstructured":"Odibat, Z., Momani, S.: The variational iteration method: an effcient scheme for handling fractional partial differential equations in fluid mechanics. Comput. Math. Appl. 58, 2199\u20132208 (2009)","journal-title":"Comput. Math. Appl."},{"key":"9631_CR17","volume-title":"The Fractional Calculus","author":"KB Oldham","year":"1974","unstructured":"Oldham, K.B., Spanier, J.: The Fractional Calculus. New\u00a0York and London, Academic Press (1974)"},{"key":"9631_CR18","volume-title":"Fractional Differential Equations","author":"I Podulbny","year":"1999","unstructured":"Podulbny, I.: Fractional Differential Equations. New\u00a0York, Academic Press (1999)"},{"key":"9631_CR19","doi-asserted-by":"crossref","first-page":"4125","DOI":"10.1016\/j.cnsns.2012.03.003","volume":"17","author":"A Saadatmandi","year":"2012","unstructured":"Saadatmandi, A., Dehghan, M., Azizi, M.R.: The Sinc\u2013Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients. Commun. Nonlinear Sci. Numer. Simulat. 17, 4125\u20134136 (2012)","journal-title":"Commun. Nonlinear Sci. Numer. Simulat."},{"key":"9631_CR20","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"SG Samko","year":"1993","unstructured":"Samko, S.G., Kilbas, A.A., Marchev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Springer-Verlag, New\u00a0York (1993)"},{"key":"9631_CR21","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/s11075-010-9393-x","volume":"56","author":"S Shen","year":"2011","unstructured":"Shen, S., Liu, F., Anh, V.: Numerical approximations and solution techniques for the space-time Riesz\u2013Caputo fractional advection-diffusion equation. Numer. Algor. 56, 383\u2013404 (2011)","journal-title":"Numer. Algor."},{"key":"9631_CR22","volume-title":"Numerical Solution of Partial Differential Equations: Finite Difference Methods","author":"GD Smith","year":"1992","unstructured":"Smith, G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd edn. Oxford University Press, Oxford (1992)","edition":"3"},{"key":"9631_CR23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.apnum.2005.03.003","volume":"56","author":"ZZ Sun","year":"2006","unstructured":"Sun, Z.Z., Wu, X.N.: A fully discrete difference scheme for a diffusion-wave system. Appl. Numer. Math. 56, 193\u2013209 (2006)","journal-title":"Appl. Numer. Math."},{"key":"9631_CR24","doi-asserted-by":"crossref","first-page":"4208","DOI":"10.1016\/j.cnsns.2011.03.021","volume":"16","author":"M Uddin","year":"2011","unstructured":"Uddin, M., Hag, S.: RBFs approximation method for time fractional partial differential equations. Commun. Nonlinear Sci. Numer. Simulat. 16, 4208\u20134214 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simulat."},{"key":"9631_CR25","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1137\/080730597","volume":"47","author":"P Zhuang","year":"2009","unstructured":"Zhuang, P., Liu, F., Anh, V., Turner, I.: Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term. SIAM J. Numer. Anal. 47, 1760\u20131781 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"9631_CR26","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1016\/j.camwa.2009.08.071","volume":"59","author":"Z Yunying","year":"2010","unstructured":"Yunying, Z., Changpin, L., Zhengang, Z.: A note on the finite element method for the space-fractional advection diffusion equation. Comput. Math. Appl. 59, 1718\u20131726 (2010)","journal-title":"Comput. Math. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9631-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9631-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9631-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:19Z","timestamp":1559365699000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9631-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,29]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["9631"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9631-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,29]]}}}