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The stability and convergence analysis of the two proposed schemes are studied by applying Fourier analysis. Finally, the effectiveness of the proposed schemes and the correctness of the theoretical results are verified by two numerical examples.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023074","type":"journal-article","created":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T10:50:31Z","timestamp":1697107831000},"page":"1692-1712","source":"Crossref","is-referenced-by-count":6,"title":["Two high-order compact difference schemes with temporal graded meshes for time-fractional Black-Scholes equation"],"prefix":"10.3934","volume":"18","author":[{"given":"Jie","family":"Gu","sequence":"first","affiliation":[{"name":"College of Science, Guilin University of Technology, Guilin, 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijuan","family":"Nong","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistic, Guangxi Normal University, Guilin, 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Yi","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistic, Guangxi Normal University, Guilin, 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"An","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Science, Guilin University of Technology, Guilin, 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023074-1","doi-asserted-by":"publisher","unstructured":"N. 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