{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:20:49Z","timestamp":1726273249314},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T00:00:00Z","timestamp":1723334400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T00:00:00Z","timestamp":1723334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s40314-024-02880-7","type":"journal-article","created":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T07:01:51Z","timestamp":1723359711000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A numerical technique for solving singularly perturbed two-point boundary value problems"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-5540-6302","authenticated-orcid":false,"given":"Pramod Chakravarthy","family":"Podila","sequence":"first","affiliation":[]},{"given":"Rahul","family":"Mishra","sequence":"additional","affiliation":[]},{"given":"Higinio","family":"Ramos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,11]]},"reference":[{"key":"2880_CR1","first-page":"90","volume":"192","author":"A Andargie","year":"2007","unstructured":"Andargie A, Reddy UN (2007a) Fitted fourth-order tridiagonal finite difference method for singular perturbation problems. Appl Math Comput 192:90\u2013100","journal-title":"Appl Math Comput"},{"key":"2880_CR2","first-page":"1767","volume":"190","author":"A Andargie","year":"2007","unstructured":"Andargie A, Reddy YN (2007b) An exponentially fitted special second-order finite difference method for solving singular perturbation problems. Appl Math Comput 190:1767\u20131782","journal-title":"Appl Math Comput"},{"issue":"2","key":"2880_CR3","first-page":"99","volume":"4","author":"HA Ashi","year":"2010","unstructured":"Ashi HA, Cummings LJ, Matthews PC (2010) Exponential time differencing methods: stability analysis and application to the nonlinear Schrodinger equation. Int J Numer Methods Appl 4(2):99\u2013128","journal-title":"Int J Numer Methods Appl"},{"key":"2880_CR4","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/S0377-0427(02)00479-X","volume":"147","author":"T Aziz","year":"2002","unstructured":"Aziz T, Khan A (2002) A spline method for second-order singularly perturbed boundary value problems. J Comput Appl Math 147:445\u2013452","journal-title":"J Comput Appl Math"},{"key":"2880_CR5","volume-title":"Advanced mathematical methods for scientists and engineers","author":"CM Bender","year":"1978","unstructured":"Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers. McGraw-Hill, New York"},{"key":"2880_CR6","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1006\/jcph.2002.6995","volume":"176","author":"SM Cox","year":"2002","unstructured":"Cox SM, Matthews PC (2002) Exponential time differencing for stiff systems. J Comput Phys 176:430\u2013455","journal-title":"J Comput Phys"},{"key":"2880_CR7","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1016\/j.cpc.2008.04.013","volume":"179","author":"F de la Hoz","year":"2008","unstructured":"de la Hoz F, Vadillo F (2008) An exponential time differencing method for the nonlinear Schr\u00f6dinger equation. Comput Phys Commun 179:449\u2013456","journal-title":"Comput Phys Commun"},{"key":"2880_CR8","first-page":"200","volume":"22","author":"Q Du","year":"2004","unstructured":"Du Q, Zhu W (2004) Stability analysis and application of exponential time differencing scheme. J Comput Math 22:200\u2013209","journal-title":"J Comput Math"},{"key":"2880_CR9","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10543-005-7141-8","volume":"45","author":"Q Du","year":"2005","unstructured":"Du Q, Zhu W (2005) Analysis and applications of the exponential time differencing schemes and their contour integration modifications. BIT Numer Math 45:307\u2013328","journal-title":"BIT Numer Math"},{"key":"2880_CR10","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/BF00939575","volume":"63","author":"MG Gasparo","year":"1998","unstructured":"Gasparo MG, Macconi M (1998) New initial value method for singularly perturbed boundary value problems. J Optim Theory Appl 63:213\u2013224","journal-title":"J Optim Theory Appl"},{"key":"2880_CR11","volume-title":"Singular perturbation theory. Mathematical and analytical techniques with applications to engineering","author":"RS Johnson","year":"2005","unstructured":"Johnson RS (2005) Singular perturbation theory. Mathematical and analytical techniques with applications to engineering. Springer, Berlin"},{"key":"2880_CR12","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10915-014-9897-y","volume":"63","author":"CY Jung","year":"2015","unstructured":"Jung CY, Nguyen TB (2015) Semi-analytical time differencing methods for stiff problems. J Sci Comput 63:355\u2013373","journal-title":"J Sci Comput"},{"key":"2880_CR13","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/BF00938946","volume":"53","author":"MK Kadalbajoo","year":"1987","unstructured":"Kadalbajoo MK, Reddy UN (1987) Initial-value technique for a class of nonlinear singular perturbation problems. J Optim Theory Appl 53:395\u2013406","journal-title":"J Optim Theory Appl"},{"key":"2880_CR14","first-page":"8645","volume":"218","author":"A Kaushik","year":"2012","unstructured":"Kaushik A, Kumar V, Vashishth AK (2012) An efficient mixed asymptotic-numerical scheme for singularly perturbed convection diffusion problems. Appl Math Comput 218:8645\u20138658","journal-title":"Appl Math Comput"},{"key":"2880_CR15","doi-asserted-by":"publisher","first-page":"2081","DOI":"10.1016\/j.apm.2014.10.019","volume":"39","author":"V Kumar","year":"2015","unstructured":"Kumar V, Srinivasan B (2015) An adaptive mesh strategy for singularly perturbed convection diffusion problems. Appl Math Model 39:2081\u20132091","journal-title":"Appl Math Model"},{"key":"2880_CR16","first-page":"8645","volume":"218","author":"V Kumar","year":"2012","unstructured":"Kumar V, Kaushik A, Vashishth AK (2012) An efficient mixed asymptotic-numerical scheme for singularly perturbed convection diffusion problems. Appl Math Comput 218:8645\u20138658","journal-title":"Appl Math Comput"},{"issue":"13","key":"2880_CR17","doi-asserted-by":"publisher","first-page":"2254","DOI":"10.3390\/math10132254","volume":"10","author":"JB Munyakazi","year":"2022","unstructured":"Munyakazi JB, Kehinde OO (2022) A new parameter uniform discretization of semilinear singularly perturbed problems. Mathematics 10(13):2254","journal-title":"Mathematics"},{"key":"2880_CR18","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1023\/A:1022639003366","volume":"97","author":"S Natesan","year":"1998","unstructured":"Natesan S, Ramanujam N (1998) Initial value technique for singularly perturbed boundary value problems for second order ordinary differential equations arising in chemical reactor theory. J Optim Theory Appl 97:455\u2013470","journal-title":"J Optim Theory Appl"},{"key":"2880_CR19","volume-title":"Introduction to perturbation techniques","author":"AH Nayfeh","year":"1981","unstructured":"Nayfeh AH (1981) Introduction to perturbation techniques. Wiley, New York"},{"key":"2880_CR20","volume-title":"Introduction to singular perturbations","author":"RE O\u2019Malley","year":"1974","unstructured":"O\u2019Malley RE (1974) Introduction to singular perturbations. Academic Press, New York"},{"key":"2880_CR21","first-page":"27","volume":"136","author":"YN Reddy","year":"2003","unstructured":"Reddy YN, Chakravarthy PP (2003) Method of reduction of order for solving singularly perturbed two-point boundary value problems. Appl Math Comput 136:27\u201345","journal-title":"Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02880-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02880-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02880-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T13:05:07Z","timestamp":1726232707000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02880-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,11]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["2880"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02880-7","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,8,11]]},"assertion":[{"value":"1 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Both authors have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"366"}}