{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T00:03:18Z","timestamp":1770681798519,"version":"3.49.0"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T00:00:00Z","timestamp":1720828800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T00:00:00Z","timestamp":1720828800000},"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":["Numer Algor"],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s11075-024-01882-0","type":"journal-article","created":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T10:01:48Z","timestamp":1720864908000},"page":"411-439","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems"],"prefix":"10.1007","volume":"99","author":[{"given":"Nirupam","family":"Sahoo","sequence":"first","affiliation":[]},{"given":"Randhir","family":"Singh","sequence":"additional","affiliation":[]},{"given":"Higinio","family":"Ramos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,13]]},"reference":[{"key":"1882_CR1","doi-asserted-by":"crossref","unstructured":"Chan, C., Hon, Y.: A constructive solution for a generalized Thomas-Fermi theory of ionized atoms. Quarterly of Applied Mathematics. 45\u00a0(3),591\u2013599","DOI":"10.1090\/qam\/910465"},{"key":"1882_CR2","doi-asserted-by":"crossref","first-page":"57","DOI":"10.2475\/ajs.s2-50.148.57","volume":"148","author":"HJ Lane","year":"1870","unstructured":"Lane, H.J.: On the theoretical temperature of the sun, under the hypothesis of a gaseous mass maintaining its volume by its internal heat, and depending on the laws of gases as known to terrestrial experiment. Am. J. Sci. 148, 57\u201374 (1870)","journal-title":"Am. J. Sci."},{"key":"1882_CR3","unstructured":"Emden, R.: Gaskugeln: Anwendungen der mechanischen W\u00e4rmetheorie auf kosmologische und meteorologische Probleme, B. Teubner (1907)"},{"issue":"1","key":"1882_CR4","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1145\/321250.321259","volume":"12","author":"RW Hockney","year":"1965","unstructured":"Hockney, R.W.: A fast direct solution of Poisson\u2019s equation using Fourier analysis. Journal of the Association for Computing Machinery. 12(1), 95\u2013113 (1965)","journal-title":"Journal of the Association for Computing Machinery."},{"key":"1882_CR5","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.cplett.2017.04.077","volume":"679","author":"A-M Wazwaz","year":"2017","unstructured":"Wazwaz, A.-M.: Solving the non-isothermal reaction-diffusion model equations in a spherical catalyst by the variational iteration method. Chem. Phys. Lett. 679, 132\u2013136 (2017)","journal-title":"Chem. Phys. Lett."},{"issue":"12","key":"1882_CR6","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1007\/s10483-013-1758-6","volume":"34","author":"K Reger","year":"2013","unstructured":"Reger, K., Van Gorder, R.: Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere. Appl. Math. Mech. 34(12), 1439\u20131452 (2013)","journal-title":"Appl. Math. Mech."},{"issue":"2","key":"1882_CR7","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/0022-5193(76)90071-0","volume":"60","author":"S Lin","year":"1976","unstructured":"Lin, S.: Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J. Theor. Biol. 60(2), 449\u2013457 (1976)","journal-title":"J. Theor. Biol."},{"key":"1882_CR8","volume-title":"The emission of electricity from hot bodies","author":"OW Richardson","year":"1921","unstructured":"Richardson, O.W.: The emission of electricity from hot bodies. Longmans, Green and Company (1921)"},{"issue":"8","key":"1882_CR9","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1080\/00207160.2015.1045888","volume":"93","author":"R Singh","year":"2016","unstructured":"Singh, R., Wazwaz, A.M., Kumar, J.: An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models. Int. J. Comput. Math. 93(8), 1330\u20131346 (2016)","journal-title":"Int. J. Comput. Math."},{"key":"1882_CR10","doi-asserted-by":"crossref","unstructured":"Singh, R., Kumar, J.: The Adomian decomposition method with Green\u2019s function for solving nonlinear singular boundary value problems.ss Journal of Applied Mathematics and Computing. 44(1\u20132), 397\u2013416 (2014)","DOI":"10.1007\/s12190-013-0699-4"},{"key":"1882_CR11","doi-asserted-by":"crossref","DOI":"10.1016\/j.jocs.2023.102041","volume":"70","author":"N Sahoo","year":"2023","unstructured":"Sahoo, N., Singh, R.: A new efficient semi-numerical method with a convergence control parameter for Lane-Emden-Fowler boundary value problem. Journal of Computational Science. 70, 102041 (2023)","journal-title":"Journal of Computational Science."},{"key":"1882_CR12","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.cam.2018.07.004","volume":"346","author":"R Singh","year":"2019","unstructured":"Singh, R., Garg, H., Guleria, V.: Haar wavelet collocation method for Lane-Emden equations with Dirichlet, Neumann and Neumann-Robin boundary conditions. J. Comput. Appl. Math. 346, 150\u2013161 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1882_CR13","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.matcom.2020.02.004","volume":"174","author":"R Singh","year":"2020","unstructured":"Singh, R., Guleria, V., Singh, M.: Haar wavelet quasilinearization method for numerical solution of Emden-Fowler type equations. Math. Comput. Simul. 174, 123\u2013133 (2020)","journal-title":"Math. Comput. Simul."},{"issue":"1","key":"1882_CR14","doi-asserted-by":"crossref","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(1), 62\u201370 (2012)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"6","key":"1882_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/s13360-020-00489-3","volume":"135","author":"J Shahni","year":"2020","unstructured":"Shahni, J., Singh, R.: An efficient numerical technique for Lane-Emden-Fowler boundary value problems: Bernstein collocation method. The European Physical Journal Plus. 135(6), 1\u201321 (2020)","journal-title":"The European Physical Journal Plus."},{"key":"1882_CR16","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2023.115701","volume":"441","author":"J Shahni","year":"2024","unstructured":"Shahni, J., Singh, R.: Numerical solution and error analysis of the Thomas-Fermi type equations with integral boundary conditions by the modified collocation techniques. J. Comput. Appl. Math. 441, 115701 (2024)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"1882_CR17","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF01390712","volume":"50","author":"S Iyengar","year":"1986","unstructured":"Iyengar, S., Jain, P.: Spline finite difference methods for singular two point boundary value problems. Numer. Math. 50(3), 363\u2013376 (1986)","journal-title":"Numer. Math."},{"key":"1882_CR18","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.apnum.2019.05.004","volume":"145","author":"P Roul","year":"2019","unstructured":"Roul, P., Thula, K., Agarwal, R.: Non-optimal fourth-order and optimal sixth-order B-spline collocation methods for Lane-Emden boundary value problems. Appl. Numer. Math. 145, 342\u2013360 (2019)","journal-title":"Appl. Numer. Math."},{"issue":"10","key":"1882_CR19","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1016\/j.cnsns.2011.02.026","volume":"16","author":"AM Wazwaz","year":"2011","unstructured":"Wazwaz, A.M.: The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models. Commun. Nonlinear Sci. Numer. Simul. 16(10), 3881\u20133886 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"6","key":"1882_CR20","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1140\/epjp\/i2017-11521-x","volume":"132","author":"R Singh","year":"2017","unstructured":"Singh, R., Das, N., Kumar, J.: The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions. The European Physical Journal Plus. 132(6), 251 (2017)","journal-title":"The European Physical Journal Plus."},{"issue":"10","key":"1882_CR21","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1007\/s10910-022-01401-3","volume":"60","author":"D Tiwari","year":"2022","unstructured":"Tiwari, D., Verma, A.K., Cattani, C.: Wavelet solution of a strongly nonlinear Lane-Emden equation. J. Math. Chem. 60(10), 2054\u20132080 (2022)","journal-title":"J. Math. Chem."},{"issue":"Suppl 1","key":"1882_CR22","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s00366-020-01155-z","volume":"38","author":"J Shahni","year":"2022","unstructured":"Shahni, J., Singh, R.: Numerical results of Emden-Fowler boundary value problems with derivative dependence using the bernstein collocation method. Engineering with Computers 38(Suppl 1), 371\u2013380 (2022)","journal-title":"Engineering with Computers"},{"key":"1882_CR23","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.apnum.2018.01.018","volume":"128","author":"KT Elgindy","year":"2018","unstructured":"Elgindy, K.T., Refat, H.M.: High-order shifted Gegenbauer integral pseudo-spectral method for solving differential equations of Lane-Emden type. Appl. Numer. Math. 128, 98\u2013124 (2018)","journal-title":"Appl. Numer. Math."},{"key":"1882_CR24","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.matcom.2021.10.023","volume":"193","author":"H Ramos","year":"2022","unstructured":"Ramos, H., Rufai, M.A.: An adaptive pair of one-step hybrid block Nystr\u00f6m methods for singular initial-value problems of Lane-Emden-Fowler type. Math. Comput. Simul. 193, 497\u2013508 (2022)","journal-title":"Math. Comput. Simul."},{"issue":"6","key":"1882_CR25","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.3390\/math11061535","volume":"11","author":"MA Rufai","year":"2023","unstructured":"Rufai, M.A., Ramos, H.: Solving SIVPs of Lane-Emden-Fowler Type Using a Pair of Optimized Nystr\u00f6m Methods with a Variable Step Size. Mathematics. 11(6), 1535 (2023)","journal-title":"Mathematics."},{"issue":"4","key":"1882_CR26","doi-asserted-by":"crossref","first-page":"2925","DOI":"10.1007\/s00366-021-01309-7","volume":"38","author":"J Shahni","year":"2022","unstructured":"Shahni, J., Singh, R.: Laguerre wavelet method for solving Thomas-Fermi type equations. Engineering with Computers 38(4), 2925\u20132935 (2022)","journal-title":"Engineering with Computers"},{"key":"1882_CR27","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.apnum.2020.02.016","volume":"153","author":"AK Dizicheh","year":"2020","unstructured":"Dizicheh, A.K., Salahshour, S., Ahmadian, A., Baleanu, D.: A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane-Emden equations. Appl. Numer. Math. 153, 443\u2013456 (2020)","journal-title":"Appl. Numer. Math."},{"key":"1882_CR28","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.apnum.2021.07.006","volume":"169","author":"M Abdelhakem","year":"2021","unstructured":"Abdelhakem, M., Youssri, Y.: Two spectral Legendre\u2019s derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems. Appl. Numer. Math. 169, 243\u2013255 (2021)","journal-title":"Appl. Numer. Math."},{"key":"1882_CR29","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.apnum.2020.07.019","volume":"158","author":"S G\u00fcmg\u00fcm","year":"2020","unstructured":"G\u00fcmg\u00fcm, S.: Taylor wavelet solution of linear and nonlinear Lane-Emden equations. Appl. Numer. Math. 158, 44\u201353 (2020)","journal-title":"Appl. Numer. Math."},{"issue":"9","key":"1882_CR30","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1007\/s10910-018-0911-8","volume":"56","author":"R Singh","year":"2018","unstructured":"Singh, R.: Optimal homotopy analysis method for the non-isothermal reaction-diffusion model equations in a spherical catalyst. J. Math. Chem. 56(9), 2579\u20132590 (2018)","journal-title":"J. Math. Chem."},{"issue":"11","key":"1882_CR31","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1140\/epjp\/i2019-13084-2","volume":"134","author":"R Singh","year":"2019","unstructured":"Singh, R.: Analytic solution of singular Emden-Fowler-type equations by Green\u2019s function and homotopy analysis method. The European Physical Journal Plus. 134(11), 583 (2019)","journal-title":"The European Physical Journal Plus."},{"issue":"3","key":"1882_CR32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40819-019-0650-y","volume":"5","author":"R Singh","year":"2019","unstructured":"Singh, R.: A modified homotopy perturbation method for nonlinear singular Lane-Emden equations arising in various physical models. International Journal of Applied and Computational Mathematics. 5(3), 1\u201315 (2019)","journal-title":"International Journal of Applied and Computational Mathematics."},{"issue":"1","key":"1882_CR33","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s10910-013-0260-6","volume":"52","author":"R Rach","year":"2014","unstructured":"Rach, R., Duan, J.S., Wazwaz, A.M.: Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J. Math. Chem. 52(1), 255\u2013267 (2014)","journal-title":"J. Math. Chem."},{"issue":"9","key":"1882_CR34","doi-asserted-by":"crossref","first-page":"2691","DOI":"10.1007\/s10910-018-0912-7","volume":"56","author":"TC Hao","year":"2018","unstructured":"Hao, T.C., Cong, F.Z., Shang, Y.-F.: An efficient method for solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions and error estimate. J. Math. Chem. 56(9), 2691\u20132706 (2018)","journal-title":"J. Math. Chem."},{"key":"1882_CR35","doi-asserted-by":"crossref","unstructured":"Flockerzi, D., Sundmacher, K.: On coupled Lane-Emden equations arising in dusty fluid models, in: Journal of Physics: Conference Series, Vol. 268, IOP Publishing, p. 012006 (2011)","DOI":"10.1088\/1742-6596\/268\/1\/012006"},{"key":"1882_CR36","doi-asserted-by":"crossref","first-page":"387","DOI":"10.15373\/2249555X\/MAY2014\/122","volume":"4","author":"S Muthukumar","year":"2014","unstructured":"Muthukumar, S., Veeramuni, M., Lakshmanan, R.: Analytical expression of concentration of substrate and oxygen in excess sludge production using Adomian decomposition method. Indian Journal of Applied Research. 4, 387\u2013391 (2014)","journal-title":"Indian Journal of Applied Research."},{"issue":"1\u20132","key":"1882_CR37","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s12190-013-0670-4","volume":"43","author":"R Singh","year":"2013","unstructured":"Singh, R., Kumar, J., Nelakanti, G.: Numerical solution of singular boundary value problems using green\u2019s function and improved decomposition method. J. Appl. Math. Comput. 43(1\u20132), 409\u2013425 (2013)","journal-title":"J. Appl. Math. Comput."},{"issue":"1","key":"1882_CR38","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/mma.2776","volume":"37","author":"A-M Wazwaz","year":"2014","unstructured":"Wazwaz, A.-M., Rach, R., Duan, J.-S.: A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method. Mathematical Methods in the Applied Sciences. 37(1), 10\u201319 (2014)","journal-title":"Mathematical Methods in the Applied Sciences."},{"issue":"4","key":"1882_CR39","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/s40819-021-01066-7","volume":"7","author":"R Singh","year":"2021","unstructured":"Singh, R., Singh, G., Singh, M.: Numerical algorithm for solution of the system of Emden-Fowler type equations. International Journal of Applied and Computational Mathematics. 7(4), 136 (2021)","journal-title":"International Journal of Applied and Computational Mathematics."},{"key":"1882_CR40","first-page":"785","volume":"73","author":"J-S Duan","year":"2015","unstructured":"Duan, J.-S., Rach, R., Wazwaz, A.-M.: Oxygen and carbon substrate concentrations in microbial floc particles by the Adomian decomposition method. MATCH Communications in Mathematical and in Computer Chemistry. 73, 785\u2013796 (2015)","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry."},{"key":"1882_CR41","first-page":"511","volume":"76","author":"AM Wazwaz","year":"2016","unstructured":"Wazwaz, A.M., Rach, R., Duan, J.-S.: Variational iteration method for solving oxygen and carbon substrate concentrations in microbial floc particles. MATCH Communications in Mathematical and in Computer Chemistry. 76, 511\u2013523 (2016)","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry."},{"issue":"3","key":"1882_CR42","first-page":"785","volume":"81","author":"R Singh","year":"2019","unstructured":"Singh, R., Wazwaz, A.-M.: An efficient algorithm for solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions: the homotopy analysis method. MATCH Communications in Mathematical and in Computer Chemistry. 81(3), 785\u2013800 (2019)","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry."},{"issue":"1","key":"1882_CR43","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1515\/nleng-2018-0062","volume":"8","author":"Y \u00d6zt\u00fcrk","year":"2019","unstructured":"\u00d6zt\u00fcrk, Y.: An efficient numerical algorithm for solving system of Lane-Emden type equations arising in engineering. Nonlinear Engineering. 8(1), 429\u2013437 (2019)","journal-title":"Nonlinear Engineering."},{"issue":"9","key":"1882_CR44","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1002\/mma.2890","volume":"37","author":"R Mohammadzadeh","year":"2014","unstructured":"Mohammadzadeh, R., Lakestani, M., Dehghan, M.: Collocation method for the numerical solutions of Lane-Emden type equations using cubic Hermite spline functions. Mathematical Methods in the Applied Sciences. 37(9), 1303\u20131717 (2014)","journal-title":"Mathematical Methods in the Applied Sciences."},{"issue":"8","key":"1882_CR45","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1007\/s10910-019-01048-7","volume":"57","author":"J-H He","year":"2019","unstructured":"He, J.-H., Ji, F.-Y.: Taylor series solution for Lane-Emden equation. J. Math. Chem. 57(8), 1932\u20131934 (2019)","journal-title":"J. Math. Chem."},{"key":"1882_CR46","doi-asserted-by":"crossref","unstructured":"Datsko, B., Kutniv, M.: Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs. Numerical Algorithms. 1\u201314 (2024)","DOI":"10.1007\/s11075-024-01820-0"},{"key":"1882_CR47","doi-asserted-by":"crossref","first-page":"463","DOI":"10.46793\/match.87-2.463A","volume":"87","author":"S Aydinlik","year":"2022","unstructured":"Aydinlik, S., Kiris, A.: First order smooth composite chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions. MATCH Communications in Mathematical and in Computer Chemistry. 87, 463\u2013476 (2022)","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry."},{"key":"1882_CR48","doi-asserted-by":"crossref","DOI":"10.1016\/j.rinp.2022.106067","volume":"43","author":"M Abdelhakem","year":"2022","unstructured":"Abdelhakem, M., Fawzy, M., El-Kady, M., Moussa, H.: An efficient technique for approximated BVPs via the second derivative Legendre polynomials pseudo-Galerkin method: Certain types of applications. Results in Physics. 43, 106067 (2022)","journal-title":"Results in Physics."},{"key":"1882_CR49","doi-asserted-by":"crossref","unstructured":"Gamal, M., El-Kady, M., Abdelhakem, M.: Solving real-life BVPs via the second derivative Chebyshev pseudo-Galerkin method. International Journal of Modern Physics C. 2450089 (2024)","DOI":"10.1142\/S012918312450089X"},{"issue":"2","key":"1882_CR50","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1007\/s10910-018-0964-8","volume":"57","author":"H Madduri","year":"2019","unstructured":"Madduri, H., Roul, P.: A fast-converging iterative scheme for solving a system of Lane-Emden equations arising in catalytic diffusion reactions. J. Math. Chem. 57(2), 570\u2013582 (2019)","journal-title":"J. Math. Chem."},{"issue":"9","key":"1882_CR51","first-page":"3201","volume":"215","author":"A Shah","year":"2010","unstructured":"Shah, A., Yuan, L., Khan, A.: Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations. Appl. Math. Comput. 215(9), 3201\u20133213 (2010)","journal-title":"Appl. Math. Comput."},{"issue":"07","key":"1882_CR52","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1142\/S0219024903002183","volume":"6","author":"B D\u00fcring","year":"2003","unstructured":"D\u00fcring, B., Fourni\u00e9, M., J\u00fcngel, A.: High order compact finite difference schemes for a nonlinear Black-Scholes equation. International Journal of Theoretical and Applied Finance. 6(07), 767\u2013789 (2003)","journal-title":"International Journal of Theoretical and Applied Finance."},{"issue":"1","key":"1882_CR53","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.cam.2006.07.006","volume":"206","author":"J Zhao","year":"2007","unstructured":"Zhao, J., Davison, M., Corless, R.M.: Compact finite difference method for American option pricing. J. Comput. Appl. Math. 206(1), 306\u2013321 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"1882_CR54","doi-asserted-by":"crossref","first-page":"5187","DOI":"10.1007\/s40314-018-0624-4","volume":"37","author":"D Mathale","year":"2018","unstructured":"Mathale, D., Dlamini, P., Khumalo, M.: Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems. Comput. Appl. Math. 37, 5187\u20135202 (2018)","journal-title":"Comput. Appl. Math."},{"issue":"1","key":"1882_CR55","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0021-9991(92)90324-R","volume":"103","author":"SK Lele","year":"1992","unstructured":"Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103(1), 16\u201342 (1992)","journal-title":"J. Comput. Phys."},{"key":"1882_CR56","first-page":"283","volume":"350","author":"P Roul","year":"2019","unstructured":"Roul, P., Goura, V.P., Agarwal, R.: 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 (2019)","journal-title":"Appl. Math. Comput."},{"key":"1882_CR57","doi-asserted-by":"crossref","unstructured":"Roul, P., Kumari, T.: A novel approach based on mixed exponential compact finite difference and oha methods for solving a class of nonlinear singular boundary value problems. International Journal of Computer Mathematics. 1\u201319 (2022)","DOI":"10.1080\/00207160.2022.2140278"},{"issue":"7","key":"1882_CR58","doi-asserted-by":"crossref","first-page":"1604","DOI":"10.1007\/s10910-023-01475-7","volume":"61","author":"P Dlamini","year":"2023","unstructured":"Dlamini, P., Malele, J., Simelane, S.: Solving singular boundary value problems using higher-order compact finite difference schemes with a novel higher-order implementation of Robin boundary conditions. J. Math. Chem. 61(7), 1604\u20131632 (2023)","journal-title":"J. Math. Chem."},{"key":"1882_CR59","unstructured":"Godunov, S.K., Ryabenkii, V.S.: Difference schemes: an introduction to the underlying theory, Elsevier (1987)"},{"issue":"4","key":"1882_CR60","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/s10910-021-01235-5","volume":"59","author":"J Shahni","year":"2021","unstructured":"Shahni, J., Singh, R.: Numerical solution of system of emden-fowler type equations by bernstein collocation method. J. Math. Chem. 59(4), 1117\u20131138 (2021)","journal-title":"J. Math. Chem."},{"key":"1882_CR61","doi-asserted-by":"crossref","unstructured":"K.\u00a0Thula, Roul, P.: A high-order b-spline collocation method for solving nonlinear singular boundary value problems arising in engineering and applied science. Mediterranean Journal of Mathematics. 15, 1\u201324 (2018)","DOI":"10.1007\/s00009-018-1220-y"},{"issue":"4","key":"1882_CR62","doi-asserted-by":"crossref","first-page":"377","DOI":"10.3390\/math7040377","volume":"7","author":"L-J Xie","year":"2019","unstructured":"Xie, L.-J., Zhou, C.-L., Xu, S.: Solving the systems of equations of Lane-Emden type by differential transform method coupled with Adomian polynomials. Mathematics. 7(4), 377 (2019)","journal-title":"Mathematics."},{"issue":"1","key":"1882_CR63","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/BF01934697","volume":"28","author":"M Chawla","year":"1988","unstructured":"Chawla, M., Subramanian, R., Sathi, H.: A fourth order method for a singular two-point boundary value problem. BIT Numer. Math. 28(1), 88\u201397 (1988)","journal-title":"BIT Numer. Math."},{"issue":"6","key":"1882_CR64","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1007\/s10910-018-0880-y","volume":"56","author":"AK Verma","year":"2018","unstructured":"Verma, A.K., Kayenat, S.: On the convergence of Mickens\u2019 type nonstandard finite difference schemes on Lane-Emden type equations. J. Math. Chem. 56(6), 1667\u20131706 (2018)","journal-title":"J. Math. Chem."},{"key":"1882_CR65","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.newast.2013.03.002","volume":"23","author":"E Doha","year":"2013","unstructured":"Doha, E., Abd-Elhameed, W., Youssri, Y.: Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type. New Astron. 23, 113\u2013117 (2013)","journal-title":"New Astron."},{"issue":"9\u201310","key":"1882_CR66","first-page":"1298","volume":"60","author":"Y Youssri","year":"2015","unstructured":"Youssri, Y., Abd-Elhameed, W., Doha, E.: Ultraspherical wavelets method for solving Lane-Emden type equations. Rom. J. Phys. 60(9\u201310), 1298\u20131314 (2015)","journal-title":"Rom. J. Phys."},{"issue":"2","key":"1882_CR67","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3390\/fractalfract7020133","volume":"7","author":"YH Youssri","year":"2023","unstructured":"Youssri, Y.H., Atta, A.G.: Spectral collocation approach via normalized shifted Jacobi polynomials for the nonlinear Lane-Emden equation with fractal-fractional derivative. Fractal and Fractional. 7(2), 133 (2023)","journal-title":"Fractal and Fractional."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01882-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01882-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01882-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T07:40:39Z","timestamp":1744616439000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01882-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,13]]},"references-count":67,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["1882"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01882-0","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,13]]},"assertion":[{"value":"6 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 July 2024","order":3,"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 known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interest"}},{"value":"The authors certify that there are no conflicts of interest to this work.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}},{"value":"Not Applicable","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}