{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:17:22Z","timestamp":1759191442635,"version":"3.37.3"},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11322113","91330203"],"award-info":[{"award-number":["11322113","91330203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we propose a class of new tailored finite point\nmethods (TFPM) for the numerical solution of parabolic equations. Our finite\npoint method has been tailored based on the local exponential basis\nfunctions. By the idea of our TFPM, we can recover all the traditional\nfinite difference schemes. We can also construct some new TFPM schemes with better stability condition and accuracy. Furthermore, combining with the Shishkin mesh technique, we construct the uniformly convergent\nTFPM scheme for the convection-dominant convection-diffusion problem. Our numerical examples show the\nefficiency and reliability of TFPM.<\/jats:p>","DOI":"10.1515\/cmam-2016-0017","type":"journal-article","created":{"date-parts":[[2016,4,27]],"date-time":"2016-04-27T09:38:21Z","timestamp":1461749901000},"page":"543-562","source":"Crossref","is-referenced-by-count":8,"title":["Tailored Finite Point Method for Parabolic Problems"],"prefix":"10.1515","volume":"16","author":[{"given":"Zhongyi","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}]},{"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}]}],"member":"374","published-online":{"date-parts":[[2016,4,27]]},"reference":[{"key":"2023033116455912187_j_cmam-2016-0017_ref_001_w2aab3b7d515b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Bakhvalov N. S.,\nOn the optimization of methods for solving boundary value problems with boundary layers,\nZh. Vychisl. Mat. Mat. Fiz. 9 (1969), 841\u2013859.","DOI":"10.1016\/0041-5553(69)90038-X"},{"key":"2023033116455912187_j_cmam-2016-0017_ref_002_w2aab3b7d515b1b6b1ab2ab2Aa","unstructured":"Dunne R. K. and O\u2019Riordan E.,\nInterior layers arising in linear singularly perturbed differential equations with discontinuous coefficients,\nProceedings of the Fourth International Conference on Finite Difference Methods: Theory and Applications (FDM \u201906),\nRousse University, Bulgaria (2007), 29\u201338."},{"key":"2023033116455912187_j_cmam-2016-0017_ref_003_w2aab3b7d515b1b6b1ab2ab3Aa","unstructured":"Farrell P. A., Hemker P. W. and Shishkin G. I.,\nDiscrete approximations for singularly perturbed boundary value problems with parabolic layers I,\nJ. Comput. Math. 14 (1996), 71\u201397."},{"key":"2023033116455912187_j_cmam-2016-0017_ref_004_w2aab3b7d515b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"Gracia J. L. and O\u2019Riordan E.,\nNumerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type,\nMath. Comp. 85 (2016), 581\u2013599.","DOI":"10.1090\/mcom\/2998"},{"key":"2023033116455912187_j_cmam-2016-0017_ref_005_w2aab3b7d515b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"Han H. and Huang Z.,\nTailored finite point method for a singular perturbation problem with variable coefficients in two dimensions,\nJ. Sci. Comput. 41 (2009), 200\u2013220.","DOI":"10.1007\/s10915-009-9292-2"},{"key":"2023033116455912187_j_cmam-2016-0017_ref_006_w2aab3b7d515b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"Han H. and Huang Z.,\nTailored finite point method for steady-state reaction-diffusion equation,\nCommun. Math. 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Math. 14 (2014), 321\u2013345.","DOI":"10.1515\/cmam-2014-0012"},{"key":"2023033116455912187_j_cmam-2016-0017_ref_010_w2aab3b7d515b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"Han H., Huang Z. and Kellogg B.,\nA Tailored finite point method for a singular perturbation problem on an unbounded domain,\nJ. Sci. Comput. 36 (2008), 243\u2013261.","DOI":"10.1007\/s10915-008-9187-7"},{"key":"2023033116455912187_j_cmam-2016-0017_ref_011_w2aab3b7d515b1b6b1ab2ac11Aa","unstructured":"Hemker P. W. and Shishkin G. I.,\nDiscrete approximation of singularly perturbed parabolic PDEs with a discontinuous initial condition,\nComput. Fluid Dyn. J. 2 (1994), 375\u2013392."},{"key":"2023033116455912187_j_cmam-2016-0017_ref_012_w2aab3b7d515b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"Huang Z.,\nTailored finite point method for the interface problem,\nNetw. Heterog. 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Nauk SSR 21 (1976), 38\u201343."}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/16\/4\/article-p543.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0017\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0017\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T23:28:34Z","timestamp":1680305314000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0017\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,27]]},"references-count":21,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,7,6]]},"published-print":{"date-parts":[[2016,10,1]]}},"alternative-id":["10.1515\/cmam-2016-0017"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2016-0017","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"type":"electronic","value":"1609-9389"},{"type":"print","value":"1609-4840"}],"subject":[],"published":{"date-parts":[[2016,4,27]]}}}