{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T11:18:30Z","timestamp":1763551110158},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671081"],"award-info":[{"award-number":["11671081"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, a high-order difference scheme is proposed for an one-dimensional space and time fractional Bloch\u2013Torrey equation.\nA third-order accurate formula, based on the weighted and shifted Gr\u00fcnwald\u2013Letnikov difference operators, is used to approximate the Caputo fractional derivative in temporal direction.\nFor the discretization of the spatial Riesz fractional derivative, we approximate the weighed values of the Riesz fractional derivative at three points by the fractional central difference operator.\nThe unique solvability, unconditional stability and convergence of the scheme are rigorously proved by the discrete energy method.\nThe convergence order is 3 in time and 4 in space in <jats:inline-formula id=\"j_cmam-2017-0034_ineq_9999_w2aab3b7e2508b1b6b1aab1c14b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>L<\/m:mi>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:msub>\n                                    <m:mi>L<\/m:mi>\n                                    <m:mn>2<\/m:mn>\n                                 <\/m:msub>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2017-0034_eq_mi604.png\" \/>\n                        <jats:tex-math>{L_{1}(L_{2})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norm.\nTwo numerical examples are implemented to testify the accuracy of the numerical solution and the efficiency of the difference scheme.<\/jats:p>","DOI":"10.1515\/cmam-2017-0034","type":"journal-article","created":{"date-parts":[[2017,9,6]],"date-time":"2017-09-06T10:00:59Z","timestamp":1504692059000},"page":"147-164","source":"Crossref","is-referenced-by-count":9,"title":["A High-Order Difference Scheme for the Space and Time Fractional Bloch\u2013Torrey Equation"],"prefix":"10.1515","volume":"18","author":[{"given":"Yun","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics , Southeast University , Nanjing 210096 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Zhong","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics , Southeast University , Nanjing 210096 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,9,6]]},"reference":[{"key":"2023033115122853284_j_cmam-2017-0034_ref_001_w2aab3b7e2508b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"S.  Bhalekar, V.  Daftardar-Gejji, D.  Baleanu and R.  Magin,\nFractional Bloch equation with delay,\nComput. Math. Appl. 61 (2011), no. 5, 1355\u20131365.","DOI":"10.1016\/j.camwa.2010.12.079"},{"key":"2023033115122853284_j_cmam-2017-0034_ref_002_w2aab3b7e2508b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"W.  Bu, Y.  Tang, Y.  Wu and J.  Yang,\nFinite difference\/finite element method for two-dimensional space and time fractional Bloch\u2013Torrey equations,\nJ. Comput. 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