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Applying the proposed scheme in temporal direction and the central difference scheme in spatial direction, a new finite difference method is developed for approximating the time fractional wave equation. The proposed method is unconditionally stable, convergent with order $$O (\\tau ^{3- \\alpha }), \\alpha \\in (1, 2)$$<\/jats:tex-math>\n \n O<\/mml:mi>\n \n (<\/mml:mo>\n \n \u03c4<\/mml:mi>\n \n 3<\/mml:mn>\n -<\/mml:mo>\n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n ,<\/mml:mo>\n \u03b1<\/mml:mi>\n \u2208<\/mml:mo>\n \n (<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n 2<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and the error has the asymptotic expansion. Richardson extrapolation is applied to improve the accuracy of the numerical method. The convergence orders are $$O ( \\tau ^{4- \\alpha })$$<\/jats:tex-math>\n \n O<\/mml:mi>\n (<\/mml:mo>\n \n \u03c4<\/mml:mi>\n \n 4<\/mml:mn>\n -<\/mml:mo>\n \u03b1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$O ( \\tau ^{2(3- \\alpha )}), \\alpha \\in (1, 2)$$<\/jats:tex-math>\n \n O<\/mml:mi>\n \n (<\/mml:mo>\n \n \u03c4<\/mml:mi>\n \n 2<\/mml:mn>\n (<\/mml:mo>\n 3<\/mml:mn>\n -<\/mml:mo>\n \u03b1<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n ,<\/mml:mo>\n \u03b1<\/mml:mi>\n \u2208<\/mml:mo>\n \n (<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n 2<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, respectively, after first two extrapolations. Numerical examples are presented to show that the numerical results are consistent with the theoretical findings.<\/jats:p>","DOI":"10.1007\/s10915-023-02395-z","type":"journal-article","created":{"date-parts":[[2023,11,23]],"date-time":"2023-11-23T09:02:30Z","timestamp":1700730150000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Unconditionally Stable and Convergent Difference Scheme for Superdiffusion with Extrapolation"],"prefix":"10.1007","volume":"98","author":[{"given":"Jinping","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles Wing Ho","family":"Green","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amiya K.","family":"Pani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5686-5017","authenticated-orcid":false,"given":"Yubin","family":"Yan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,11,23]]},"reference":[{"key":"2395_CR1","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1080\/01630563.2015.1078815","volume":"37","author":"A Chen","year":"2016","unstructured":"Chen, A., Li, C.: Numerical solution of fractional diffusion-wave equation. 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