{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:02:58Z","timestamp":1763535778598},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"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":[[2021,6]]},"DOI":"10.1007\/s12190-020-01444-2","type":"journal-article","created":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T11:02:34Z","timestamp":1603537354000},"page":"527-542","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Approximate solution of singular IVPs of Lane\u2013Emden type and error estimation via advanced Adomian decomposition method"],"prefix":"10.1007","volume":"66","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":[[2020,10,24]]},"reference":[{"key":"1444_CR1","doi-asserted-by":"publisher","first-page":"57","DOI":"10.2475\/ajs.s2-50.148.57","volume":"50","author":"JH Lane","year":"1870","unstructured":"Lane, J.H.: On the theoretical temperature of the sun. Am. J. Sci. Arts 50, 57\u201374 (1870)","journal-title":"Am. J. Sci. Arts"},{"key":"1444_CR2","unstructured":"Emden, R.: Gaskugein: Anwendugen der mechanischen warmetheoric. B.G, Tewbner, Leipzig and Berlin (1907)"},{"key":"1444_CR3","volume-title":"Introduction to Non-linear Differential and Integral Equations","author":"HT Davis","year":"1962","unstructured":"Davis, H.T.: Introduction to Non-linear Differential and Integral Equations. Dover, New York (1962)"},{"key":"1444_CR4","volume-title":"Introduction to Study of Stellar Structure","author":"S Chandrasekhar","year":"1967","unstructured":"Chandrasekhar, S.: Introduction to Study of Stellar Structure. Dover, New York (1967)"},{"key":"1444_CR5","volume-title":"The emission of electricity from hot bodies","author":"OU Richardson","year":"1921","unstructured":"Richardson, O.U.: The emission of electricity from hot bodies. Longman, Green and Co., London (1921)"},{"key":"1444_CR6","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/j.physleta.2007.02.002","volume":"365","author":"MSH Chowdhury","year":"2007","unstructured":"Chowdhury, M.S.H., Hashim, I.: Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Phys. Lett. A 365, 439\u2013447 (2007)","journal-title":"Phys. Lett. A"},{"key":"1444_CR7","first-page":"148","volume":"160","author":"GP Horedt","year":"1986","unstructured":"Horedt, G.P.: Exact solutions of the Lane\u2013Emden equation in N-dimensional space. Astron. Astrophys. 160, 148\u2013156 (1986)","journal-title":"Astron. Astrophys."},{"key":"1444_CR8","first-page":"359","volume":"172","author":"GP Horedt","year":"1987","unstructured":"Horedt, G.P.: Approximate analytical solutions of the Lane\u2013Emden equation in N-dimensional space. Astron. Astrophys. 172, 359\u2013367 (1987)","journal-title":"Astron. Astrophys."},{"key":"1444_CR9","doi-asserted-by":"publisher","unstructured":"Umesh, Kumar, M.: Numerical solution of Lane-Emden type equations using Adomian decomposition method with unequal step-size partitions. Eng. Comput. (2020). https:\/\/doi.org\/10.1108\/EC-02-2020-0073","DOI":"10.1108\/EC-02-2020-0073"},{"key":"1444_CR10","doi-asserted-by":"publisher","first-page":"28","DOI":"10.4236\/am.2013.410A3005","volume":"4","author":"PPC Alzate","year":"2013","unstructured":"Alzate, P.P.C., Urue\u00f1a, W.A.: The Zhou\u2019s method for solving the White-Dwarfs equation. Appl. Math. 4, 28\u201332 (2013)","journal-title":"Appl. Math."},{"issue":"7","key":"1444_CR11","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1016\/j.newast.2008.01.002","volume":"13","author":"CM Khalique","year":"2008","unstructured":"Khalique, C.M., Ntsime, P.: Exact solutions of the Lane\u2013Emden type equations. New Astron. 13(7), 476\u2013480 (2008)","journal-title":"New Astron."},{"key":"1444_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2013\/507145","volume":"2013","author":"H Aminikhah","year":"2013","unstructured":"Aminikhah, H., Moradian, S.: Numerical solution of singular Lane\u2013Emden equation. ISRN Math. Phys. 2013, 1\u20139 (2013)","journal-title":"ISRN Math. Phys."},{"key":"1444_CR13","first-page":"1","volume":"174","author":"Y Khan","year":"2012","unstructured":"Khan, Y., Svoboda, Z., Smarda, Z.: Solving certain classes of Lane\u2013Emden type equations using the differential transformation method. Adv. Differ. Equ. 174, 1\u201311 (2012)","journal-title":"Adv. Differ. Equ."},{"key":"1444_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2011\/479396","volume":"2011","author":"M Yigider","year":"2011","unstructured":"Yigider, M., Tabatabaei, K., Celik, E.: The numerical method for solving differential equations of Lane\u2013Emden type by Pad\u2019e approximation. Discrete Dyn. Nat. Soc. 2011, 1\u20139 (2011)","journal-title":"Discrete Dyn. Nat. Soc."},{"key":"1444_CR15","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.cnsns.2011.04.025","volume":"17","author":"AH Bhrawy","year":"2012","unstructured":"Bhrawy, A.H., Alofi, A.S.: A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations. Commun. Nonlinear Sci. Numer. Simul. 17, 62\u201370 (2012)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"4","key":"1444_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10509-018-3286-1","volume":"363","author":"H Singh","year":"2018","unstructured":"Singh, H.: An efficient computational method for the approximate solution of nonlinear Lane\u2013Emden type equations arising in astrophysics. Astrophys. Space Sci. 363(4), 1\u201310 (2018)","journal-title":"Astrophys. Space Sci."},{"issue":"2","key":"1444_CR17","doi-asserted-by":"publisher","first-page":"98","DOI":"10.7763\/IJAPM.2013.V3.184","volume":"3","author":"FK Yin","year":"2013","unstructured":"Yin, F.K., Han, W.Y., Song, J.Q.: Modified Laplace decomposition method for Lane-Emden type differential equations. Int. J. Appl. Phys. Math. 3(2), 98\u2013102 (2013)","journal-title":"Int. J. Appl. Phys. Math."},{"key":"1444_CR18","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.nonrwa.2007.08.017","volume":"10","author":"MSH Chowdhury","year":"2009","unstructured":"Chowdhury, M.S.H., Hashim, I.: Solutions of Emden-Fowler equations by homotopy-perturbation method. Nonlinear Anal. Real World Appl. 10, 104\u2013115 (2009)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"1444_CR19","doi-asserted-by":"publisher","first-page":"8830","DOI":"10.1016\/j.jcp.2009.08.029","volume":"228","author":"K Parand","year":"2009","unstructured":"Parand, K., Shahini, M., Dehghan, M.: Rational Legendre pseudospectral approach for solving non-linear differential equations of Lane\u2013Emden type. J. Comput. Phys. 228, 8830\u20138840 (2009)","journal-title":"J. Comput. Phys."},{"key":"1444_CR20","doi-asserted-by":"publisher","unstructured":"Mohanty, R., Ghosh, B.P.: Absolute stability of an implicit method based on third-order off-step discretization for the initial-value problem on a graded mesh. Eng. Comput. (2019). https:\/\/doi.org\/10.1007\/s0036-019-00857-3","DOI":"10.1007\/s0036-019-00857-3"},{"key":"1444_CR21","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/j.amc.2003.12.047","volume":"161","author":"JI Ramos","year":"2005","unstructured":"Ramos, J.I.: Linearization techniques for singular initial-value problems of ordinary differential equations. Appl. Math. Comput. 161, 525\u2013542 (2005)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"1444_CR22","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/S0010-4655(01)00415-5","volume":"141","author":"VB Mandelzweig","year":"2001","unstructured":"Mandelzweig, V.B., Tabakin, F.: Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs. Comput. Phys. Commun. 141(2), 268\u2013281 (2001)","journal-title":"Comput. Phys. Commun."},{"issue":"1","key":"1444_CR23","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1080\/00207160.2015.1100299","volume":"94","author":"JS Duan","year":"2015","unstructured":"Duan, J.S., Rach, R., Wazwaz, A.M.: Higher-order numeric solutions of the Lane\u2013Emden type equations derived from the multi-stage modified Adomian decomposition method. Int. J. Comput. Math. 94(1), 197\u2013215 (2015)","journal-title":"Int. J. Comput. Math."},{"issue":"4","key":"1444_CR24","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1515\/nleng-2017-0086","volume":"7","author":"H Aminikhah","year":"2018","unstructured":"Aminikhah, H.: Solutions of the singular IVPs of Lane\u2013Emden type equations by combining Laplace transformation and perturbation technique. Nonlinear Eng. 7(4), 273\u2013278 (2018)","journal-title":"Nonlinear Eng."},{"issue":"7","key":"1444_CR25","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1063\/1.528326","volume":"30","author":"CM Bender","year":"1989","unstructured":"Bender, C.M., Milton, K.A., Pinsky, S.S., Simmons, J.L.M.: A new perturbative approach to non linear problems. J. Math. Phys. 30(7), 1447\u20131455 (1989)","journal-title":"J. Math. Phys."},{"issue":"1","key":"1444_CR26","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.E.: A modified decomposition. Comput. Math. Appl. 23(1), 17\u201323 (1992)","journal-title":"Comput. Math. Appl."},{"issue":"10","key":"1444_CR27","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.: Nonlinear transformation of series-part II. Comput. Math. Appl. 23(10), 79\u201383 (1992)","journal-title":"Comput. Math. Appl."},{"key":"1444_CR28","doi-asserted-by":"crossref","first-page":"6337","DOI":"10.1016\/j.amc.2011.01.007","volume":"217","author":"JS Duan","year":"2011","unstructured":"Duan, J.S.: Convenient analytic recurrence algorithms for the Adomian polynomials. Appl. Math. Comput. 217, 6337\u20136348 (2011)","journal-title":"Appl. Math. Comput."},{"key":"1444_CR29","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.: A convenient computational form for the Adomian polynomials. J. Math. Anal. Appl. 102, 415\u2013419 (1984)","journal-title":"J. Math. Anal. Appl."},{"issue":"5","key":"1444_CR30","doi-asserted-by":"publisher","first-page":"562","DOI":"10.9734\/BJMCS\/2015\/14067","volume":"5","author":"M Kaliyappan","year":"2015","unstructured":"Kaliyappan, M., Hariharan, S.: Symbolic computation of Adomian polynomials based on Rach\u2019s rule. Br. J. Math. Comput. Sci. 5(5), 562\u2013570 (2015)","journal-title":"Br. J. Math. Comput. Sci."},{"key":"1444_CR31","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.geomphys.2019.06.004","volume":"144","author":"JG Liu","year":"2019","unstructured":"Liu, J.G., Yang, X.J., Feng, Y.Y.: On integrability of the time fractional nonlinear heat conduction equation. J. Geom. Phys. 144, 190\u2013198 (2019)","journal-title":"J. Geom. Phys."},{"key":"1444_CR32","doi-asserted-by":"publisher","unstructured":"Al-sawalha, M.M.: Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control. Adv. Differ. Equ. (2019). https:\/\/doi.org\/10.1186\/s1362-020-0287-7","DOI":"10.1186\/s1362-020-0287-7"},{"key":"1444_CR33","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/j.matcom.2020.07.005","volume":"178","author":"JG Liu","year":"2020","unstructured":"Liu, J.G., Yang, X.J., Feng, Y.Y., Cui, P.: On group analysis of the time fractional extended (2+1)-dimensional Zakharov-Kuznetsov equation in quantum magneto-plasmas. Math. Comput. Simul. 178, 407\u2013421 (2020)","journal-title":"Math. Comput. Simul."},{"key":"1444_CR34","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.cjph.2020.05.006","volume":"66","author":"YY Feng","year":"2020","unstructured":"Feng, Y.Y., Yang, X.J., Liu, J.G.: On overall behavior of Maxwell mechanical model by the combined Caputo fractional derivative. Chin. J. Phys. 66, 269\u2013276 (2020)","journal-title":"Chin. J. Phys."},{"issue":"12","key":"1444_CR35","first-page":"103","volume":"18","author":"Y Cherruault","year":"1993","unstructured":"Cherruault, Y., Adomian, G.: Decomposition methods: a new proof of convergence. Comput. Math. Appl. 18(12), 103\u2013106 (1993)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"1444_CR36","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1002\/num.20549","volume":"27","author":"A Abdelrazec","year":"2009","unstructured":"Abdelrazec, A., Pelinovsky, D.: Convergence of the Adomian decomposition method for initial-value problems. Numer. Methods Partial Differ. Equ. 27(4), 749\u2013766 (2009)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"1444_CR37","doi-asserted-by":"publisher","unstructured":"Umesh, Kumar,M.:Numerical solution of singular boundary value problems using advanced Adomian decomposition method. Eng. Comput. (2020). https:\/\/doi.org\/10.1007\/s0036-020-00972-6","DOI":"10.1007\/s0036-020-00972-6"},{"issue":"11","key":"1444_CR38","first-page":"2264","volume":"32","author":"SS Ray","year":"2014","unstructured":"Ray, S.S.: New approach for general convergence of the Adomian decomposition method. World Appl. Sci. J. 32(11), 2264\u20132268 (2014)","journal-title":"World Appl. Sci. J."},{"key":"1444_CR39","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/BF01436325","volume":"18","author":"GJ Cooper","year":"1971","unstructured":"Cooper, G.J.: Error bounds for numerical solutions of ordinary differential equation. Numer. Math. 18, 162\u2013170 (1971)","journal-title":"Numer. Math."},{"key":"1444_CR40","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1016\/j.camwa.2005.12.004","volume":"52","author":"PG Warne","year":"2006","unstructured":"Warne, P.G., Polignone, W.D.A., Sochacki, J.S., Parker, G.E., Carothers, D.C.: Explicit A\u2014priori error bounds and Adaptive error control for approximation of non-linear initial value differential systems. Comput. Math. Appl. 52, 1695\u20131710 (2006)","journal-title":"Comput. Math. Appl."},{"key":"1444_CR41","doi-asserted-by":"publisher","first-page":"2218","DOI":"10.1002\/mma.1519","volume":"34","author":"S Yuzbasi","year":"2011","unstructured":"Yuzbasi, S.: A numerical approach for solving a class of the nonlinear Lane\u2013Emden type equations arising in astrophysics. Math. Methods Appl. Sci. 34, 2218\u20132230 (2011)","journal-title":"Math. Methods Appl. Sci."},{"key":"1444_CR42","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0096-3003(99)00223-4","volume":"118","author":"AM Wazwaz","year":"2001","unstructured":"Wazwaz, A.M.: A new algorithm for solving differential equations of Lane\u2013Emden type. Appl. Math. Comput. 118, 287\u2013310 (2001)","journal-title":"Appl. Math. Comput."},{"key":"1444_CR43","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/s40314-013-0084-9","volume":"33","author":"EH Doha","year":"2014","unstructured":"Doha, E.H., Bhrawy, A.H., Hafez, R.M., Gorder, R.A.: A Jacobi rational pseudospectral method for Lane\u2013Emden initial value problems arising in astrophysics on a semi-infinite interval. Comput. Appl. Math. 33, 607\u2013619 (2014)","journal-title":"Comput. Appl. Math."},{"key":"1444_CR44","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.amc.2014.08.085","volume":"247","author":"S Mall","year":"2014","unstructured":"Mall, S., Chakraverty, S.: Chebyshev neural network based model for solving Lane\u2013Emden type equations. Appl. Math. Comput. 247, 100\u2013114 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"1444_CR45","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.newast.2011.09.005","volume":"17","author":"RK Pandey","year":"2012","unstructured":"Pandey, R.K., Kumar, N.: Solution of Lane\u2013Emden type equations using Bernstein operational matrix of differentiation. New Astron. 17(3), 303\u2013308 (2012)","journal-title":"New Astron."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01444-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01444-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01444-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T00:26:18Z","timestamp":1698279978000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01444-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,24]]},"references-count":45,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1444"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01444-2","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,24]]},"assertion":[{"value":"8 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}