{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T05:13:27Z","timestamp":1782364407101,"version":"3.54.5"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T00:00:00Z","timestamp":1585267200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T00:00:00Z","timestamp":1585267200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Department of Science and Technology (DST INSPIRE), New Delhi, India","doi-asserted-by":"publisher","award":["IF160648"],"award-info":[{"award-number":["IF160648"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s12190-020-01340-9","type":"journal-article","created":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T06:02:57Z","timestamp":1585288977000},"page":"813-828","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition"],"prefix":"10.1007","volume":"63","author":[{"given":"Devendra","family":"Kumar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6941-2463","authenticated-orcid":false,"given":"Parvin","family":"Kumari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,3,27]]},"reference":[{"key":"1340_CR1","first-page":"977","volume":"3","author":"R Almomani","year":"2012","unstructured":"Almomani, R., Almefleh, H.: On heat conduction problem with integral boundary condition. J. Emerg. Trends Eng. Appl. Sci. 3, 977\u2013979 (2012)","journal-title":"J. Emerg. Trends Eng. Appl. Sci."},{"key":"1340_CR2","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1007\/BF02456971","volume":"23","author":"GM Amiraliyev","year":"2002","unstructured":"Amiraliyev, G.M., \u00c7akir, M.: Numerical solution of the singularly perturbed problem with nonlocal boundary condition. Appl. Math. Mech. (Engl. Ed.) 23, 755\u2013764 (2002)","journal-title":"Appl. Math. Mech. (Engl. Ed.)"},{"key":"1340_CR3","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2013-173","author":"A Ashyralyev","year":"2013","unstructured":"Ashyralyev, A., Sharifov, Y.A.: Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and integral boundary conditions. Adv. Differ. Equ. (2013). https:\/\/doi.org\/10.1186\/1687-1847-2013-173","journal-title":"Adv. Differ. Equ."},{"key":"1340_CR4","doi-asserted-by":"publisher","first-page":"2623","DOI":"10.1016\/j.na.2007.08.041","volume":"69","author":"D Bahuguna","year":"2008","unstructured":"Bahuguna, D., Abbas, S., Dabas, J.: Partial functional differential equation with an integral boundary condition and applications to popoulation dynamics. Nonlinear Anal. 69, 2623\u20132635 (2008)","journal-title":"Nonlinear Anal."},{"key":"1340_CR5","first-page":"7","volume":"8","author":"D Bahuguna","year":"2008","unstructured":"Bahuguna, D., Dabas, J.: Existence and uniqueness of a solution to a semilinear partial delay differential equation with an integral condition. Nonlinear Dyn. Syst. Theory 8, 7\u201319 (2008)","journal-title":"Nonlinear Dyn. Syst. Theory"},{"key":"1340_CR6","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.na.2007.12.007","volume":"70","author":"A Boucherif","year":"2009","unstructured":"Boucherif, A.: Second order boundary value problems with integral boundary condition. Nonlinear Anal. 70, 368\u2013379 (2009)","journal-title":"Nonlinear Anal."},{"key":"1340_CR7","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/BF02254673","volume":"1","author":"SA Brykalov","year":"1994","unstructured":"Brykalov, S.A.: A second order nonlinear problem with two-point and integral boundary conditions. Georg. Math. J. 1, 243\u2013249 (1994)","journal-title":"Georg. Math. J."},{"key":"1340_CR8","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1137\/0732025","volume":"32","author":"B Cahlon","year":"1995","unstructured":"Cahlon, B., Kulkarni, D.M., Shi, P.: Stepwise stability for the heat equation with a nonlocal constraint. SIAM J. Numer. Anal. 32, 571\u2013593 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"1340_CR9","first-page":"539","volume":"160","author":"M \u00c7akir","year":"2005","unstructured":"\u00c7akir, M., Amiraliyev, G.M.: A finite difference method for the singularly perturbed problem with nonlocal boundary condition. Appl. Math. Comput. 160, 539\u2013549 (2005)","journal-title":"Appl. Math. Comput."},{"key":"1340_CR10","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1090\/qam\/160437","volume":"21","author":"JR Cannon","year":"1963","unstructured":"Cannon, J.R.: The solution of the heat equation subject to the specification of energy. Q. Appl. Math. 21, 155\u2013160 (1963)","journal-title":"Q. Appl. Math."},{"key":"1340_CR11","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/S0025-5564(00)00006-7","volume":"165","author":"RV Culshaw","year":"2000","unstructured":"Culshaw, R.V., Ruan, S.: A delay differential equation model of HIV infection of $$CD4^+$$ T-cells. Math. Biosci. 165, 27\u201339 (2000)","journal-title":"Math. Biosci."},{"key":"1340_CR12","first-page":"1","volume":"2000","author":"M Denche","year":"2000","unstructured":"Denche, M., Marhoune, A.L.: High-order mixed-type differential equations with weighted integral boundary conditions. Electron. J. Differ. Equ. 2000, 1\u201310 (2000)","journal-title":"Electron. J. Differ. Equ."},{"key":"1340_CR13","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 Press, Dublin (1980)"},{"key":"1340_CR14","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0309-1708(91)90055-S","volume":"14","author":"RE Ewing","year":"1991","unstructured":"Ewing, R.E., Lin, T.: A class of parameter estimation techniques for fluid flow in porous media. Adv. Water Res. 14, 89\u201397 (1991)","journal-title":"Adv. Water Res."},{"key":"1340_CR15","doi-asserted-by":"publisher","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":"1340_CR16","doi-asserted-by":"publisher","first-page":"1759","DOI":"10.1090\/S0025-5718-05-01764-3","volume":"74","author":"PA Farrell","year":"2005","unstructured":"Farrell, P.A., O\u2019Riordan, E., Shishkin, G.I.: A class of singularly perturbed semilinear differential equations with interior layers. Math. Comput. 74, 1759\u20131776 (2005)","journal-title":"Math. Comput."},{"key":"1340_CR17","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s007910050030","volume":"2","author":"L Formaggia","year":"1999","unstructured":"Formaggia, L., Nobil, F., Quarteroni, A., Venezian, A.: Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Vis. Sci. 2, 75\u201383 (1999)","journal-title":"Comput. Vis. Sci."},{"key":"1340_CR18","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1216\/rmjm\/1021477351","volume":"30","author":"JM Gallardo","year":"2000","unstructured":"Gallardo, J.M.: Second order differential operators with integral boundary conditions and generation of semigroups. Rocky Mt. J. Math. 30, 1265\u20131292 (2000)","journal-title":"Rocky Mt. J. Math."},{"key":"1340_CR19","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1023\/A:1023631706975","volume":"117","author":"VY Glizer","year":"2003","unstructured":"Glizer, V.Y.: Asymptotic analysis and solution of a finite-horizon $$H_{\\infty }$$ control problem for singularly perturbed linear systems with small state delay. J. Optim. Theory Appl. 117, 295\u2013325 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"1340_CR20","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0021-9045(68)90025-7","volume":"1","author":"CA Hall","year":"1968","unstructured":"Hall, C.A.: On error bounds for spline interpolation. J. Approx. Theory 1, 209\u2013218 (1968)","journal-title":"J. Approx. Theory"},{"key":"1340_CR21","first-page":"43","volume":"31","author":"M Hu","year":"2013","unstructured":"Hu, M., Wang, L.: Triple positive solutions for an impulsive dynamic equation with integral boundary condition on time scales. Int. J. Appl. Math. Stat. 31, 43\u201366 (2013)","journal-title":"Int. J. Appl. Math. Stat."},{"key":"1340_CR22","first-page":"820","volume":"27","author":"NI Ionkin","year":"1991","unstructured":"Ionkin, N.I., Furletov, D.G.: Uniform stability of difference schemes for a nonlocal nonselfadjoint boundary value problem with variable coefficients. Differ. Equ. 27, 820\u2013826 (1991)","journal-title":"Differ. Equ."},{"key":"1340_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-0427(02)00371-0","volume":"147","author":"T Jankowskii","year":"2002","unstructured":"Jankowskii, T.: Differential equations with integral boundary conditions. J. Comput. Appl. Math. 147, 1\u20138 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"1340_CR24","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":"1340_CR25","first-page":"248","volume":"179","author":"MK Kadalbajoo","year":"2006","unstructured":"Kadalbajoo, M.K., Patidar, K.C.: $$\\varepsilon $$-Uniform fitted mesh finite difference methods for general singular perturbation problems. Appl. Math. Comput. 179, 248\u2013266 (2006)","journal-title":"Appl. Math. Comput."},{"key":"1340_CR26","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1590\/S0101-82052005000200001","volume":"24","author":"MK Kadalbajoo","year":"2005","unstructured":"Kadalbajoo, M.K., Sharma, K.K.: Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations. Comput. Appl. Math. 24, 151\u2013172 (2005)","journal-title":"Comput. Appl. Math."},{"key":"1340_CR27","first-page":"90","volume":"204","author":"MK Kadalbajoo","year":"2008","unstructured":"Kadalbajoo, M.K., Kumar, D.: Fitted mesh B-spline collocation method for singularly perturbed differential-difference equations with small delay. Appl. Math. Comput. 204, 90\u201398 (2008)","journal-title":"Appl. Math. Comput."},{"key":"1340_CR28","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s12190-018-1174-z","volume":"59","author":"D Kumar","year":"2019","unstructured":"Kumar, D., Kumari, P.: A parameter-uniform numerical scheme for the parabolic singularly perturbed initial boundary value problems with large time delay. J. Appl. Math. Comput. 59, 179\u2013206 (2019)","journal-title":"J. Appl. Math. Comput."},{"key":"1340_CR29","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1080\/10236198.2018.1543417","volume":"24","author":"D Kumar","year":"2018","unstructured":"Kumar, D.: A collocation method for singularly perturbed differential-difference turning point problems exhibiting boundary\/interior layers. J. Differ. Equ. Appl. 24, 1847\u20131870 (2018)","journal-title":"J. Differ. Equ. Appl."},{"key":"1340_CR30","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1186\/1687-2770-2012-147","volume":"2012","author":"H Li","year":"2012","unstructured":"Li, H., Sun, F.: Existence of solutions for integral boundary value problems of second order ordinary differential equations. Bound. Value Probl. 2012, 147 (2012). https:\/\/doi.org\/10.1186\/1687-2770-2012-147","journal-title":"Bound. Value Probl."},{"key":"1340_CR31","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1515\/GMJ.2000.133","volume":"7","author":"A Lomtatidze","year":"2000","unstructured":"Lomtatidze, A., Malaguti, L.: On a nonlocal boundary-value problems for second order nonlinear singular differential equations. Georg. Math. J. 7, 133\u2013154 (2000)","journal-title":"Georg. Math. J."},{"key":"1340_CR32","doi-asserted-by":"publisher","DOI":"10.1142\/2933","volume-title":"Fitted Numerical Methods for Singular Perturbation Problems","author":"JJH Miller","year":"1996","unstructured":"Miller, J.J.H., O\u2019Riordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore (1996)"},{"key":"1340_CR33","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1515\/cmam-2012-0001","volume":"13","author":"S Nicaise","year":"2013","unstructured":"Nicaise, S., Xenophontos, C.: Robust approximation of singularly perturbed delay differential equations by the hp finite element method. Comput. Methods Appl. Math. 13, 21\u201337 (2013)","journal-title":"Comput. Methods Appl. Math."},{"key":"1340_CR34","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/S0377-0427(00)00614-2","volume":"136","author":"CV Pao","year":"2001","unstructured":"Pao, C.V.: Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions. J. Comput. Appl. Math. 136, 227\u2013243 (2001)","journal-title":"J. Comput. Appl. Math."},{"key":"1340_CR35","first-page":"1","volume":"10","author":"AK Rahmat","year":"2003","unstructured":"Rahmat, A.K.: The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions. Electron. J. Qual. Theory. Differ. Equ. 10, 1\u201315 (2003)","journal-title":"Electron. J. Qual. Theory. Differ. Equ."},{"key":"1340_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03206-0","volume-title":"Numerical Methods for Singularly Perturbed Differential Equations, Convection\u2013Diffusion and Flow Problems","author":"HG Roos","year":"1996","unstructured":"Roos, H.G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations, Convection\u2013Diffusion and Flow Problems. Springer, Berlin (1996)"},{"key":"1340_CR37","volume-title":"Macro-to-Microscale Heat Transfer","author":"DY Tzou","year":"1997","unstructured":"Tzou, D.Y.: Macro-to-Microscale Heat Transfer. Taylor and Francis, Washington (1997)"},{"key":"1340_CR38","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0024-3795(75)90112-3","volume":"11","author":"JM Varah","year":"1975","unstructured":"Varah, J.M.: A lower bound for the smallest singular value of a matrix. Linear Algebra Appl. 11, 3\u20135 (1975)","journal-title":"Linear Algebra Appl."},{"key":"1340_CR39","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.aml.2014.06.013","volume":"38","author":"H Zarin","year":"2014","unstructured":"Zarin, H.: On discontinuous Galerkin finite element method for singularly perturbed delay differential equations. Appl. Math. Lett. 38, 27\u201332 (2014)","journal-title":"Appl. Math. Lett."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01340-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-020-01340-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01340-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,27]],"date-time":"2021-03-27T01:14:37Z","timestamp":1616807677000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-020-01340-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,27]]},"references-count":39,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["1340"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01340-9","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,27]]},"assertion":[{"value":"20 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}