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In this paper, in order to solve the fractional advection-diffusion equation, the fractional characteristic finite difference method is presented, which is based on the method of characteristics (MOC) and fractional finite difference (FD) procedures. The stability, consistency, convergence, and error estimate of the method are obtained. An example is also given to illustrate the applicability of theoretical results.<\/jats:p>","DOI":"10.1155\/2013\/648595","type":"journal-article","created":{"date-parts":[[2013,3,24]],"date-time":"2013-03-24T17:01:00Z","timestamp":1364144460000},"page":"1-8","source":"Crossref","is-referenced-by-count":1,"title":["A High-Accuracy MOC\/FD Method for Solving Fractional Advection-Diffusion Equations"],"prefix":"10.1155","volume":"2013","author":[{"given":"Lijuan","family":"Su","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3615-5624","authenticated-orcid":true,"given":"Pei","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1029\/2000WR900031","volume":"36","year":"2000","journal-title":"Water Resources Research"},{"volume":"2012","journal-title":"Discrete Dynamics in Nature and Society","year":"2012","key":"6"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.06.005"},{"year":"2006","key":"10"},{"year":"1974","key":"13"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/903518"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/161246"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/050642757"},{"year":"1999","key":"14"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1063\/1.527251"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.12.043"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/0517050"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.02.011"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/080714130"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.01.033"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6239"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1137\/060673114"},{"key":"18","first-page":"1022","volume":"39","year":"2003","journal-title":"Water Resources Research"},{"issue":"48","key":"25","doi-asserted-by":"crossref","first-page":"4405","DOI":"10.1016\/j.physleta.2009.10.004","volume":"373","year":"2009","journal-title":"Physics Letters A"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596309396"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/0719063"},{"year":"1994","key":"12"},{"key":"7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0024-3795(75)90112-3","volume":"11","year":"1975","journal-title":"Linear Algebra and Its Applications"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05156-2"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903428281"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/648595.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/648595.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/648595.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T05:57:06Z","timestamp":1498024626000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/648595\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":25,"alternative-id":["648595","648595"],"URL":"https:\/\/doi.org\/10.1155\/2013\/648595","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}