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For one\u2010dimensional (1D) problems, with a function transformation, we construct an indirect compact difference (ICD) method, which requires less calculation cost than the corresponding DCD method, and prove under the appropriate conditions that ICD method has second\u2010order (resp. forth\u2010order) calculation accuracy in time (resp. space). By extending the argument for 1D case, we further obtain an ICD method for solving two\u2010dimensional (2D) problems and derive the similar convergence result. For ICD and DCD methods of 2D problems, we also give their alternative direction implicit (ADI) schemes. Moreover, for the fast implementations of ICD method of 1D problems and indirect ADI method of 2D problems, we further present their acceleration strategies. Finally, with a series of numerical experiments, the findings in this paper are further confirmed.<\/jats:p>","DOI":"10.1002\/nla.2556","type":"journal-article","created":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T07:47:47Z","timestamp":1713253667000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Accelerated schemes of compact difference methods for space\u2010fractional sine\u2010Gordon equations with distributed delay"],"prefix":"10.1002","volume":"31","author":[{"given":"Tao","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China"},{"name":"Department of Mathematics University of Macau Macao China"}]},{"given":"Chengjian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China"},{"name":"Hubei Key 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