{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T15:52:39Z","timestamp":1768837959605,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T00:00:00Z","timestamp":1581984000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T00:00:00Z","timestamp":1581984000000},"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":["Engineering with Computers"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00366-020-00972-6","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T08:04:51Z","timestamp":1582013091000},"page":"2853-2863","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Numerical solution of singular boundary value problems using advanced Adomian decomposition method"],"prefix":"10.1007","volume":"37","author":[{"family":"Umesh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoj","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,18]]},"reference":[{"issue":"4","key":"972_CR1","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1002\/num.20549","volume":"27","author":"A Abdelrazec","year":"2011","unstructured":"Abdelrazec A, Pelinovsky D (2011) Convergence of the adomian decomposition method for initial-value problems. Numer Methods Partial Differ Equ 27(4):749\u2013766","journal-title":"Numer Methods Partial Differ Equ"},{"key":"972_CR2","volume-title":"Solving Frontier problems of physics: the decomposition method","author":"G Adomian","year":"2013","unstructured":"Adomian G (2013) Solving Frontier problems of physics: the decomposition method, vol 60. Springer, Berlin"},{"issue":"10","key":"972_CR3","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0898-1221(92)90058-P","volume":"23","author":"G Adomian","year":"1992","unstructured":"Adomian G, Rach R (1992) Nonlinear transformation of series-part II. Comput Math Appl 23(10):79\u201383","journal-title":"Comput Math Appl"},{"issue":"1","key":"972_CR4","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s00366-018-0591-9","volume":"35","author":"P Assari","year":"2019","unstructured":"Assari P, Dehghan M (2019) Application of dual-Chebyshev wavelets for the numerical solution of boundary integral equations with logarithmic singular kernels. Eng Comput 35(1):175\u2013190","journal-title":"Eng Comput"},{"issue":"1","key":"972_CR5","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/BF01934697","volume":"28","author":"M Chawla","year":"1988","unstructured":"Chawla M, Subramanian R, Sathi H (1988) A fourth order method for a singular two-point boundary value problem. BIT Numer Math 28(1):88\u201397","journal-title":"BIT Numer Math"},{"issue":"12","key":"972_CR6","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/0895-7177(93)90233-O","volume":"18","author":"Y Cherruault","year":"1993","unstructured":"Cherruault Y, Adomian G (1993) Decomposition methods: a new proof of convergence. Math Comput Model 18(12):103\u2013106","journal-title":"Math Comput Model"},{"issue":"2","key":"972_CR7","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/BF01436325","volume":"18","author":"G Cooper","year":"1971","unstructured":"Cooper G (1971) Error bounds for numerical solutions of ordinary differential equations. Numerische Mathematik 18(2):162\u2013170","journal-title":"Numerische Mathematik"},{"issue":"13","key":"972_CR8","first-page":"6337","volume":"217","author":"JS Duan","year":"2011","unstructured":"Duan JS (2011) Convenient analytic recurrence algorithms for the Adomian polynomials. Appl Math Comput 217(13):6337\u20136348","journal-title":"Appl Math Comput"},{"issue":"2","key":"972_CR9","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/S0022-5193(75)80131-7","volume":"54","author":"U Flesch","year":"1975","unstructured":"Flesch U (1975) The distribution of heat sources in the human head: a theoretical consideration. J Theor Biol 54(2):285\u2013287","journal-title":"J Theor Biol"},{"key":"972_CR10","first-page":"562","volume":"5","author":"M Kaliyappan","year":"2015","unstructured":"Kaliyappan M, Hariharan S (2015) Symbolic computation of Adomian polynomials based on Rach\u2019s rule. J Adv Math Comput Sci 5:562\u2013570","journal-title":"J Adv Math Comput Sci"},{"issue":"3","key":"972_CR11","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1016\/j.camwa.2010.05.029","volume":"60","author":"AR Kanth","year":"2010","unstructured":"Kanth AR, Aruna K (2010) He\u2019s variational iteration method for treating nonlinear singular boundary value problems. Comput Math Appl 60(3):821\u2013829","journal-title":"Comput Math Appl"},{"issue":"01","key":"972_CR12","doi-asserted-by":"publisher","first-page":"1350052","DOI":"10.1142\/S0219876213500527","volume":"11","author":"S Khuri","year":"2014","unstructured":"Khuri S, Sayfy A (2014) Numerical solution for the nonlinear Emden\u2013Fowler type equations by a fourth-order adaptive method. Int J Comput Methods 11(01):1350052","journal-title":"Int J Comput Methods"},{"issue":"3\u20134","key":"972_CR13","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1016\/j.mcm.2010.04.009","volume":"52","author":"SA Khuri","year":"2010","unstructured":"Khuri SA, Sayfy A (2010) A novel approach for the solution of a class of singular boundary value problems arising in physiology. Math Comput Model 52(3\u20134):626\u2013636","journal-title":"Math Comput Model"},{"issue":"11","key":"972_CR14","doi-asserted-by":"publisher","first-page":"1750","DOI":"10.1016\/j.compchemeng.2010.02.035","volume":"34","author":"M Kumar","year":"2010","unstructured":"Kumar M, Singh N (2010) Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems. Comput Chem Eng 34(11):1750\u20131760","journal-title":"Comput Chem Eng"},{"issue":"2","key":"972_CR15","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1016\/0022-5193(76)90071-0","volume":"60","author":"S Lin","year":"1976","unstructured":"Lin S (1976) Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J Theor Biol 60(2):449\u2013457","journal-title":"J Theor Biol"},{"key":"972_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-019-00835-9","author":"Y Lotfi","year":"2017","unstructured":"Lotfi Y, Parand K, Rashedi K, Rad JA (2019) Numerical study of temperature distribution in an inverse moving boundary problem using a meshless method. Eng Comput. https:\/\/doi.org\/10.1007\/s00366-019-00835-9","journal-title":"Eng Comput"},{"issue":"2","key":"972_CR17","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/0022-5193(78)90270-9","volume":"71","author":"D McElwain","year":"1978","unstructured":"McElwain D (1978) A re-examination of oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics. J Theor Biol 71(2):255\u2013263","journal-title":"J Theor Biol"},{"key":"972_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-019-00857-3","author":"R Mohanty","year":"2019","unstructured":"Mohanty R, Ghosh BP (2019) Absolute stability of an implicit method based on third-order off-step discretization for the initial-value problem on a graded mesh. Eng Comput. https:\/\/doi.org\/10.1007\/s00366-019-00857-3","journal-title":"Eng Comput"},{"key":"972_CR19","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.cam.2017.09.040","volume":"331","author":"J Niu","year":"2018","unstructured":"Niu J, Xu M, Lin Y, Xue Q (2018) Numerical solution of nonlinear singular boundary value problems. J Comput Appl Math 331:42\u201351","journal-title":"J Comput Appl Math"},{"issue":"1\u20132","key":"972_CR20","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1080\/00207169708804603","volume":"65","author":"R Pandey","year":"1997","unstructured":"Pandey R (1997) A finite difference method for a class of singular two point boundary value problems arising in physiology. Int J Comput Math 65(1\u20132):131\u2013140","journal-title":"Int J Comput Math"},{"issue":"2","key":"972_CR21","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1016\/0022-247X(84)90181-1","volume":"102","author":"R Rach","year":"1984","unstructured":"Rach R (1984) A convenient computational form for the Adomian polynomials. J Math Anal Appl 102(2):415\u2013419","journal-title":"J Math Anal Appl"},{"issue":"1","key":"972_CR22","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0898-1221(92)90076-T","volume":"23","author":"R Rach","year":"1992","unstructured":"Rach R, Adomian G, Meyers R (1992) A modified decomposition. Comput Math Appl 23(1):17\u201323","journal-title":"Comput Math Appl"},{"issue":"11","key":"972_CR23","first-page":"2264","volume":"32","author":"SS Ray","year":"2014","unstructured":"Ray SS (2014) New approach for general convergence of the Adomian decomposition method. World Appl Sci J 32(11):2264\u20132268","journal-title":"World Appl Sci J"},{"key":"972_CR24","first-page":"283","volume":"350","author":"P Roul","year":"2019","unstructured":"Roul P, Goura VP, Agarwal R (2019) A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions. Appl Math Comput 350:283\u2013304","journal-title":"Appl Math Comput"},{"key":"972_CR25","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1016\/j.cam.2018.04.056","volume":"343","author":"P Roul","year":"2018","unstructured":"Roul P, Thula K (2018) A new high-order numerical method for solving singular two-point boundary value problems. J Comput Appl Math 343:556\u2013574","journal-title":"J Comput Appl Math"},{"issue":"1","key":"972_CR26","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1137\/0712002","volume":"12","author":"R Russell","year":"1975","unstructured":"Russell R, Shampine L (1975) Numerical methods for singular boundary value problems. SIAM J Numer Anal 12(1):13\u201336","journal-title":"SIAM J Numer Anal"},{"issue":"4","key":"972_CR27","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.1016\/j.cpc.2014.01.002","volume":"185","author":"R Singh","year":"2014","unstructured":"Singh R, Kumar J (2014) An efficient numerical technique for the solution of nonlinear singular boundary value problems. Comput Phys Commun 185(4):1282\u20131289","journal-title":"Comput Phys Commun"},{"key":"972_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2012\/541083","volume":"2012","author":"R Singh","year":"2012","unstructured":"Singh R, Kumar J, Nelakanti G (2012) New approach for solving a class of doubly singular two-point boundary value problems using Adomian decomposition method. Adv Numer Anal 2012:1\u201322","journal-title":"Adv Numer Anal"},{"issue":"12","key":"972_CR29","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1016\/j.camwa.2005.12.004","volume":"52","author":"PG Warne","year":"2006","unstructured":"Warne PG, Warne DP, Sochacki JS, Parker GE, Carothers DC (2006) Explicit a-priori error bounds and adaptive error control for approximation of nonlinear initial value differential systems. Comput Math Appl 52(12):1695\u20131710","journal-title":"Comput Math Appl"},{"issue":"1","key":"972_CR30","doi-asserted-by":"publisher","first-page":"1066","DOI":"10.1186\/s40064-016-2753-9","volume":"5","author":"Lj Xie","year":"2016","unstructured":"Xie Lj, Zhou Cl, Xu S (2016) An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method. SpringerPlus 5(1):1066","journal-title":"SpringerPlus"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-020-00972-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-020-00972-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-020-00972-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T11:25:53Z","timestamp":1631532353000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-020-00972-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,18]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["972"],"URL":"https:\/\/doi.org\/10.1007\/s00366-020-00972-6","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,18]]},"assertion":[{"value":"10 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}