{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T10:28:39Z","timestamp":1749810519919,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"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":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s12190-023-01939-8","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T14:02:19Z","timestamp":1701439339000},"page":"4645-4664","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A novel fitted spline method for the numerical treatment of singularly perturbed differential equations having small delays"],"prefix":"10.1007","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5735-545X","authenticated-orcid":false,"given":"Rakesh","family":"Ranjan","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"1939_CR1","first-page":"245","volume":"14","author":"M Adilaxmi","year":"2019","unstructured":"Adilaxmi, M., Bhargavi, D., Reddy, Y.N.: An initial value technique using exponentially fitted non standard finite difference method for singularly perturbed differential difference equations. Appl. Appl. Math. 14, 245\u2013269 (2019)","journal-title":"Appl. Appl. Math."},{"key":"1939_CR2","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1093\/comjnl\/12.2.151","volume":"12","author":"EL Albasiny","year":"1969","unstructured":"Albasiny, E.L., Hoskins, W.D.: Cubic spline solutions to two-point boundary value problems. Comput. J. 12, 151\u2013153 (1969)","journal-title":"Comput. J."},{"issue":"3\u20134","key":"1939_CR3","first-page":"419","volume":"39","author":"MA Angasu","year":"2021","unstructured":"Angasu, M.A., Duressa, G.F., Woldaregay, M.M.: Exponentially fitted numerical scheme for singularly perturbed differential equations involving small delays. J. Appl. Math. Inform. 39(3\u20134), 419\u2013435 (2021)","journal-title":"J. Appl. Math. Inform."},{"key":"1939_CR4","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1002\/andp.200451607-806","volume":"13","author":"M Bestehorn","year":"2004","unstructured":"Bestehorn, M., Grigorieva, E.V.: Formation and propagation of localized states in extended systems. Annalen der Physik. (Leipzig) 13, 423\u2013431 (2004)","journal-title":"Annalen der Physik. (Leipzig)"},{"key":"1939_CR5","volume-title":"Uniform Numerical Methods for Problems with Initial and Boundary Layers","author":"EP Doolan","year":"1980","unstructured":"Doolan, E.P., Miller, J.J.H., Schilders, W.H.A.: Uniform Numerical Methods for Problems with Initial and Boundary Layers. Boole, Dublin (1980)"},{"issue":"1","key":"1939_CR6","first-page":"86","volume":"7","author":"GF Duressa","year":"2015","unstructured":"Duressa, G.F., Reddy, Y.N.: Domain decomposition method for singularly perturbed differential difference equations with layer behaviour. Int. J. Eng. Appl. Sci. 7(1), 86\u2013102 (2015)","journal-title":"Int. J. Eng. Appl. Sci."},{"key":"1939_CR7","volume-title":"Introduction to the Theory and Application of Differential Equations with Deviating Arguments","author":"LE El\u2019sgol\u2019ts","year":"1973","unstructured":"El\u2019sgol\u2019ts, L.E., Norkin, S.B.: Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Academic Press, New York (1973)"},{"key":"1939_CR8","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1103\/RevModPhys.61.41","volume":"61","author":"DD Joseph","year":"1989","unstructured":"Joseph, D.D., Preziosi, L.: Heat waves. Rev. Mod. Phys. 61, 41\u201373 (1989)","journal-title":"Rev. Mod. Phys."},{"key":"1939_CR9","first-page":"1816","volume":"188","author":"MK Kadalbajoo","year":"2007","unstructured":"Kadalbajoo, M.K., Ramesh, V.P.: Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy. Appl. Math. Comput. 188, 1816\u20131831 (2007)","journal-title":"Appl. Math. Comput."},{"key":"1939_CR10","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1090\/S0025-5718-1978-0483484-9","volume":"32","author":"T Kellogg","year":"1978","unstructured":"Kellogg, T., Tsan, A.: Analysis of some difference approximations for a singular perturbation problem without turning point. Math. Comput. 32, 1025\u20131039 (1978)","journal-title":"Math. Comput."},{"issue":"3\u20134","key":"1939_CR11","first-page":"73","volume":"7","author":"D Kumar","year":"2012","unstructured":"Kumar, D., Kadalbajoo, M.K.: Numerical treatment of singularly perturbed delay differential equations using B-Spline collocation method on Shishkin mesh. J. Numer. Anal. Ind. Appl. Math. 7(3\u20134), 73\u201390 (2012)","journal-title":"J. Numer. Anal. Ind. Appl. Math."},{"key":"1939_CR12","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1016\/j.ijengsci.2005.05.010","volume":"43","author":"Q Liu","year":"2005","unstructured":"Liu, Q., Wang, X., De Kee, D.: Mass transport through swelling membranes. Int. J. Eng. Sci. 43, 1464\u20131470 (2005)","journal-title":"Int. J. Eng. Sci."},{"key":"1939_CR13","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1126\/science.267326","volume":"197","author":"MC Mackey","year":"1977","unstructured":"Mackey, M.C., Glass, L.: Oscillations and chaos in physiological control systems. Science 197, 287\u2013289 (1977)","journal-title":"Science"},{"key":"1939_CR14","doi-asserted-by":"publisher","DOI":"10.1142\/8410","volume-title":"Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions","author":"JJH Miller","year":"2012","unstructured":"Miller, J.J.H., O\u2019Riordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions. World Scientific (2012)"},{"key":"1939_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0977-5","volume-title":"Singular Perturbation Methods for Ordinary Differential Equations","author":"RE O\u2019Malley","year":"1991","unstructured":"O\u2019Malley, R.E.: Singular Perturbation Methods for Ordinary Differential Equations. Springer (1991)"},{"key":"1939_CR16","first-page":"1","volume":"1344","author":"K Phaneendra","year":"2019","unstructured":"Phaneendra, K., Lalu, M.: Numerical solution of singularly perturbed delay differential equations using Gaussion quadrature method. IOP J. Phys. Conf. Ser. 1344, 1\u201313 (2019)","journal-title":"IOP J. Phys. Conf. Ser."},{"key":"1939_CR17","first-page":"21","volume":"9","author":"R Ranjan","year":"2020","unstructured":"Ranjan, R., Prasad, H.S., Alam, Md.J.: A fitted numerical method for a class of singularly perturbed convection delayed dominated diffusion equation. Appl. Math. Comput. Intell. 9, 21\u201338 (2020)","journal-title":"Appl. Math. Comput. Intell."},{"key":"1939_CR18","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s12190-020-01397-6","volume":"65","author":"R Ranjan","year":"2021","unstructured":"Ranjan, R., Prasad, H.S.: A novel approach for the numerical approximation to the solution of singularly perturbed differential\u2013difference equations with small shifts. J. Appl. Math. Comput. 65, 403\u2013427 (2021)","journal-title":"J. Appl. Math. Comput."},{"issue":"3","key":"1939_CR19","first-page":"631","volume":"60","author":"DA Turuna","year":"2020","unstructured":"Turuna, D.A., Woldaregay, M.M., Duressa, G.F.: Uniformly convergent numerical method for singularly perturbed convection\u2013diffusion problems. Kyungpook Math. J. 60(3), 631\u2013647 (2020)","journal-title":"Kyungpook Math. J."},{"key":"1939_CR20","volume-title":"Micro-to-macro Scale Heat Transfer","author":"DY Tzou","year":"1997","unstructured":"Tzou, D.Y.: Micro-to-macro Scale Heat Transfer. Taylor & Francis, Washington, DC (1997)"},{"issue":"2","key":"1939_CR21","first-page":"223","volume":"38","author":"MM Woldaregay","year":"2019","unstructured":"Woldaregay, M.M., Duressa, G.F.: Parameter uniform numerical method for singularly perturbed differential difference equations. J. Niger. Math. Soc. 38(2), 223\u2013245 (2019)","journal-title":"J. Niger. Math. Soc."},{"issue":"1","key":"1939_CR22","doi-asserted-by":"publisher","first-page":"65","DOI":"10.46793\/KgJMat2201.065W","volume":"46","author":"MM Woldaregay","year":"2022","unstructured":"Woldaregay, M.M., Duressa, G.F.: Uniformly convergent numerical method for singularly perturbed delay parabolic differential equations arising in computational neuroscience. Kragujevac J. Math. 46(1), 65\u201384 (2022)","journal-title":"Kragujevac J. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01939-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-023-01939-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01939-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T13:27:23Z","timestamp":1703165243000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-023-01939-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["1939"],"URL":"https:\/\/doi.org\/10.1007\/s12190-023-01939-8","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2023,12]]},"assertion":[{"value":"27 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}