{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T16:22:53Z","timestamp":1784650973267,"version":"3.55.0"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T00:00:00Z","timestamp":1584921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFB0305601 and 2017YFB0701700"],"award-info":[{"award-number":["2017YFB0305601 and 2017YFB0701700"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Space non-integer order convection\u2013diffusion descriptions are generalized form of integer order convection\u2013diffusion problems expressing super diffusive and convective transport processes. In this article, we propose finite difference approximation for space fractional convection\u2013diffusion model having space variable coefficients on the given bounded domain over time and space. It is shown that the Crank\u2013Nicolson difference scheme based on the right shifted Gr\u00fcnwald\u2013Letnikov difference formula is unconditionally stable and it is also of second order consistency both in temporal and spatial terms with extrapolation to the limit approach. Numerical experiments are tested to verify the efficiency of our theoretical analysis and confirm order of convergence.<\/jats:p>","DOI":"10.3390\/sym12030485","type":"journal-article","created":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T13:04:04Z","timestamp":1585055044000},"page":"485","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Finite Difference Approximation Method for a Space Fractional Convection\u2013Diffusion Equation with Variable Coefficients"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3723-0059","authenticated-orcid":false,"given":"Eyaya Fekadie","family":"Anley","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"},{"name":"College of Natural and Computational Science, Department of Mathematics, Arba-Minch University, Arba-Minch 21, Ethiopia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8792-6310","authenticated-orcid":false,"given":"Zhoushun","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Diethelm, K. 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