{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T13:10:28Z","timestamp":1724073028433},"reference-count":52,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971010"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,8]]},"abstract":"Abstract<\/jats:title>Time\u2013space fractional Fokker\u2013Planck equations (TSFFPEs) are a class of very useful models for describing some practical phenomena in statistical physics. In the present article, we focus on the fast computation for semilinear two\u2010dimensional TSFFPEs. A stable implicit difference scheme with second\u2010order accuracy in time and space is derived. In order to accelerate the convergence rate of the scheme, a preconditioned strategy combining the Kronecker product splitting preconditioner and the generalized minimal residual method is suggested. Numerical experiments further confirm the theoretical accuracy of the difference scheme and computational advantage of the acceleration scheme.<\/jats:p>","DOI":"10.1002\/nla.2357","type":"journal-article","created":{"date-parts":[[2020,12,18]],"date-time":"2020-12-18T05:29:00Z","timestamp":1608269340000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A preconditioned implicit difference scheme for semilinear two\u2010dimensional time\u2013space fractional Fokker\u2013Planck equations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-9016-5631","authenticated-orcid":false,"given":"Chengjian","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China"},{"name":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China"}]},{"given":"Yongtao","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China"},{"name":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China"}]}],"member":"311","published-online":{"date-parts":[[2020,12,16]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/080714130"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2012.02.025"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-0104(02)00557-8"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.09.001"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02936089"},{"key":"e_1_2_7_7_1","first-page":"91","article-title":"Analytical solution of space\u2010time fractional Fokker Planck equations by generalized differential transform method","volume":"66","author":"Garg M","year":"2011","journal-title":"Le Matematiche"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.09.040"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/464321"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.01.067"},{"volume-title":"The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order","year":"1974","author":"Oldham K","key":"e_1_2_7_11_1"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.06.046"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1105700"},{"key":"e_1_2_7_14_1","first-page":"197","article-title":"An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data","volume":"36","author":"Jin B","year":"2015","journal-title":"IMA J Numer Anal"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.11.017"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.09.031"},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.01.033"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2005.02.008"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/140961560"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2015-02917-2"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1137\/130933447"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2014.11.007"},{"key":"e_1_2_7_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.10.053"},{"key":"e_1_2_7_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.10.005"},{"key":"e_1_2_7_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.07.045"},{"key":"e_1_2_7_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.11.034"},{"key":"e_1_2_7_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.02.025"},{"key":"e_1_2_7_28_1","doi-asserted-by":"publisher","DOI":"10.4208\/eajam.060815.180116a"},{"key":"e_1_2_7_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-014-0467-3"},{"key":"e_1_2_7_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1960"},{"key":"e_1_2_7_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-016-0128-5"},{"key":"e_1_2_7_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.11.037"},{"key":"e_1_2_7_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.03.017"},{"key":"e_1_2_7_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.01.034"},{"key":"e_1_2_7_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-019-00773-z"},{"key":"e_1_2_7_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.02.014"},{"key":"e_1_2_7_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.07.040"},{"key":"e_1_2_7_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2007.11.005"},{"key":"e_1_2_7_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2014.11.007"},{"key":"e_1_2_7_40_1","doi-asserted-by":"publisher","DOI":"10.1515\/fca-2016-0080"},{"key":"e_1_2_7_41_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1131829"},{"key":"e_1_2_7_42_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082329"},{"key":"e_1_2_7_43_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1070323"},{"key":"e_1_2_7_44_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1118816"},{"key":"e_1_2_7_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2020.04.006"},{"key":"e_1_2_7_46_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-015-0041-3"},{"key":"e_1_2_7_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0388-9"},{"key":"e_1_2_7_48_1","doi-asserted-by":"publisher","DOI":"10.1137\/0727022"},{"key":"e_1_2_7_49_1","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"e_1_2_7_50_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479802417106"},{"volume-title":"An Introduction to Numerical Analysis","year":"1989","author":"Atkinson KE","key":"e_1_2_7_51_1"},{"key":"e_1_2_7_52_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371"},{"key":"e_1_2_7_53_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198504207.001.0001","volume-title":"Iterative Methods for Toeplitz Systems","author":"Ng M","year":"2004"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2357","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/nla.2357","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2357","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T12:55:05Z","timestamp":1724072105000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.2357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,16]]},"references-count":52,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1002\/nla.2357"],"URL":"https:\/\/doi.org\/10.1002\/nla.2357","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"type":"print","value":"1070-5325"},{"type":"electronic","value":"1099-1506"}],"subject":[],"published":{"date-parts":[[2020,12,16]]},"assertion":[{"value":"2020-01-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-11-16","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-12-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}