{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T03:11:04Z","timestamp":1769051464676,"version":"3.49.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T00:00:00Z","timestamp":1590710400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T00:00:00Z","timestamp":1590710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s12190-020-01370-3","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T19:02:53Z","timestamp":1590778973000},"page":"591-614","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["SDFEM for singularly perturbed boundary-value problems with two parameters"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7385-6104","authenticated-orcid":false,"given":"D.","family":"Avijit","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7527-1989","authenticated-orcid":false,"given":"S.","family":"Natesan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,29]]},"reference":[{"key":"1370_CR1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.apnum.2017.09.005","volume":"123","author":"S Becher","year":"2018","unstructured":"Becher, S.: Analysis of Galerkin and streamline-diffusion FEMs on piecewise equidistant meshes for turning point problems exhibiting an interior layer. Appl. Num. Math. 123, 121\u2013136 (2018)","journal-title":"Appl. Num. Math."},{"key":"1370_CR2","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.amc.2016.01.060","volume":"282","author":"M Brdar","year":"2016","unstructured":"Brdar, M., Zarin, H.: On graded meshes for a two-parameter singularly perturbed problem. Appl. Math. Comput. 282, 97\u2013107 (2016)","journal-title":"Appl. Math. Comput."},{"key":"1370_CR3","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.cam.2015.07.011","volume":"292","author":"M Brdar","year":"2016","unstructured":"Brdar, M., Zarin, H.: A singularly perturbed problem with two parameters on a Bakhvalov-type mesh. J. Compu. Appl. Math. 292, 307\u2013319 (2016)","journal-title":"J. Compu. Appl. Math."},{"key":"1370_CR4","doi-asserted-by":"publisher","unstructured":"Brenner, S., Scott, R.: The mathematical theory of finite element methods. vol 15 Text in Applied Mathematics, 3rd ed., Springer-Verlag, New York (2008). https:\/\/doi.org\/10.1007\/978-0-387-75934-0","DOI":"10.1007\/978-0-387-75934-0"},{"key":"1370_CR5","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s10915-011-9489-z","volume":"50","author":"F Celiker","year":"2012","unstructured":"Celiker, F., Zhang, Z., Zhu, H.: Nodal superconvergence of SDFEM for singularly perturbed problems. J. Sci. Comput. 50, 405\u2013433 (2012)","journal-title":"J. Sci. Comput."},{"issue":"1\u20132","key":"1370_CR6","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s12190-012-0611-7","volume":"41","author":"P Das","year":"2013","unstructured":"Das, P., Natesan, S.: A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary-value problems. J. Appl. Math. Comput. 41(1\u20132), 447\u2013471 (2013)","journal-title":"J. Appl. Math. Comput."},{"key":"1370_CR7","doi-asserted-by":"crossref","DOI":"10.1201\/9781482285727","volume-title":"Robust Computational Techniques for Boundary Layers","author":"PA Farrell","year":"2000","unstructured":"Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O\u2019Riordan, E., Shishkin, G.I.: Robust Computational Techniques for Boundary Layers. Chapman & Hall\/CRC, Boca Raton (2000)"},{"key":"1370_CR8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0045-7825(82)90071-8","volume":"32","author":"TJR Hughes","year":"1982","unstructured":"Hughes, T.J.R., Brooks, A.N.: Streamline upwind\/Petrov\u2013Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier\u2013Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199\u2013259 (1982)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1370_CR9","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1016\/j.cma.2006.11.013","volume":"196","author":"V John","year":"2007","unstructured":"John, V., Knobloch, P.: On spurious oscillations at layers diminishing (SOLD) methods for convection\u2013diffusion equations: part I-A review. Comput. Methods Appl. Mech. Eng. 196, 2197\u20132215 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1370_CR10","first-page":"491","volume":"7","author":"T Lin\u00df","year":"2010","unstructured":"Lin\u00df, T.: The necessity of Shishkin decompositions. Appl. Math. Lett. 7, 491\u2013506 (2010)","journal-title":"Appl. Math. Lett."},{"key":"1370_CR11","first-page":"891","volume":"14","author":"T Lin\u00df","year":"2001","unstructured":"Lin\u00df, T.: A posteriori error estimation for a singularly perturbed problem with two small parameters. Int. J. Numer. Anal. Model. 14, 891\u2013896 (2001)","journal-title":"Int. J. Numer. Anal. Model."},{"issue":"2","key":"1370_CR12","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.jmaa.2003.08.017","volume":"289","author":"T Lin\u00df","year":"2004","unstructured":"Lin\u00df, T., Roos, H.G.: Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters. J. Math. Anal. Appl. 289(2), 355\u2013366 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"1370_CR13","doi-asserted-by":"publisher","unstructured":"Liu, L.B., Leng, H., Long, G.: Analysis of the SDFEM for singularly perturbed differential\u2013difference equations. Calcolo. 55, 23 (2018). https:\/\/doi.org\/10.1007\/s10092-018-0265-4","DOI":"10.1007\/s10092-018-0265-4"},{"issue":"1","key":"1370_CR14","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1023\/A:1021744025980","volume":"99","author":"S Natesan","year":"1998","unstructured":"Natesan, S., Ramanujam, N.: Initial-value technique for singularly-perturbed turning-point problems exhibiting twin boundary layers. J. Optim. Theory Appl. 99(1), 37\u201352 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"1370_CR15","volume-title":"Introduction to Singular Perturbations","author":"RE O\u2019Malley Jr","year":"1974","unstructured":"O\u2019Malley Jr., R.E.: Introduction to Singular Perturbations. Academic Press, New York (1974)"},{"key":"1370_CR16","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.cam.2018.08.004","volume":"347","author":"E O\u2019Riordan","year":"2019","unstructured":"O\u2019Riordan, E., Pickett, M.L.: Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem. J. Comput. Appl. Math. 347, 128\u2013149 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1370_CR17","volume-title":"Robust Numerical Methods for Singularly Perturbed Differential Equations","author":"HG Roos","year":"2008","unstructured":"Roos, H.G., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations. Springer, Berlin (2008)"},{"issue":"1","key":"1370_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4208\/jcm.1405-m4362","volume":"33","author":"HG Roos","year":"2015","unstructured":"Roos, H.G., Teofanov, Lj, Uzelac, Z.: Graded meshes for higher order FEM. J. Comput. Math. 33(1), 1\u201316 (2015)","journal-title":"J. Comput. Math."},{"key":"1370_CR19","doi-asserted-by":"crossref","first-page":"443","DOI":"10.2478\/cmam-2003-0029","volume":"3","author":"HG Roos","year":"2003","unstructured":"Roos, H.G., Uzelac, Z.: The SDFEM for a convection\u2013diffusion problem with two small parameters. Comput. Methods Appl. Math. 3, 443\u2013458 (2003)","journal-title":"Comput. Methods Appl. Math."},{"key":"1370_CR20","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0377-0427(02)00568-X","volume":"150","author":"HG Roos","year":"2003","unstructured":"Roos, H.G., Zarin, H.: The streamline\u2013diffusion method for a convection\u2013diffusion problem with a point source. J. Comput. Appl. Math. 150, 109\u2013128 (2003)","journal-title":"J. Comput. Appl. Math."},{"issue":"1\u20132","key":"1370_CR21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF02896460","volume":"22","author":"V Shanthi","year":"2006","unstructured":"Shanthi, V., Ramanujam, N., Natesan, S.: Fitted mesh method for singularly perturbed reaction-convection-diffusion problems with boundary and interior layers. J. Appl. Math. Comput. 22(1\u20132), 49\u201365 (2006)","journal-title":"J. Appl. Math. Comput."},{"key":"1370_CR22","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1007\/s12190-020-01334-7","volume":"63","author":"G Singh","year":"2020","unstructured":"Singh, G., Natesan, S.: Study of the NIPG method for two-parameter singular perturbation problems on several layer adapted grids. J. Appl. Math. Comput. 63, 683\u2013705 (2020). https:\/\/doi.org\/10.1007\/s12190-020-01334-7","journal-title":"J. Appl. Math. Comput."},{"issue":"2","key":"1370_CR23","first-page":"145","volume":"7","author":"GI \u0160i\u0161kin","year":"1976","unstructured":"\u0160i\u0161kin, G.I., Titov, V.A.: A difference scheme for a differential equation with two small parameters at the derivatives. \u010cisl. Metody Meh. Splo\u0161n. Sredy 7(2), 145\u2013155 (1976)","journal-title":"\u010cisl. Metody Meh. Splo\u0161n. Sredy"},{"issue":"5","key":"1370_CR24","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1137\/S0036142902404728","volume":"41","author":"M Stynes","year":"2003","unstructured":"Stynes, M., Tobiska, L.: The SDFEM for a convection\u2013diffusion problem with a boundary layer: Optimal error analysis and enhancement of accuracy. SIAM J. Numer. Anal. 41(5), 1620\u20131642 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"1370_CR25","doi-asserted-by":"crossref","first-page":"2109","DOI":"10.1016\/j.camwa.2010.07.052","volume":"60","author":"M Turkyilmazoglu","year":"2010","unstructured":"Turkyilmazoglu, M.: Series solution of nonlinear two-point singularly perturbed boundary layer problems. Comput. Math. Appl. 60, 2109\u20132114 (2010)","journal-title":"Comput. Math. Appl."},{"key":"1370_CR26","doi-asserted-by":"crossref","first-page":"3879","DOI":"10.1016\/j.apm.2011.02.011","volume":"35","author":"M Turkyilmazoglu","year":"2011","unstructured":"Turkyilmazoglu, M.: Analytic approximate solutions of parameterized unperturbed and singularly perturbed boundary value problems. Appl. Math. Modell. 35, 3879\u20133886 (2011)","journal-title":"Appl. Math. Modell."},{"key":"1370_CR27","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.apnum.2017.06.003","volume":"120","author":"H Zarin","year":"2017","unstructured":"Zarin, H.: Exponentially graded mesh for a singularly perturbed problem with two small parameters. Appl. Numer. Math. 120, 233\u2013242 (2017)","journal-title":"Appl. Numer. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01370-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01370-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01370-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T23:19:12Z","timestamp":1622243952000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01370-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,29]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["1370"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01370-3","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,29]]},"assertion":[{"value":"11 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}