{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T03:07:30Z","timestamp":1770692850850,"version":"3.49.0"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T00:00:00Z","timestamp":1739318400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T00:00:00Z","timestamp":1739318400000},"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":[[2026,2]]},"DOI":"10.1007\/s11075-025-02025-9","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T23:36:36Z","timestamp":1739316996000},"page":"847-882","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Compact finite difference schemes and error estimation for third-order Emden-Fowler equations"],"prefix":"10.1007","volume":"101","author":[{"given":"Nirupam","family":"Sahoo","sequence":"first","affiliation":[]},{"given":"Randhir","family":"Singh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,12]]},"reference":[{"issue":"6","key":"2025_CR1","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1016\/j.newast.2012.02.003","volume":"17","author":"K Boubaker","year":"2012","unstructured":"Boubaker, K., Van Gorder, R.A.: Application of the BPES to Lane\u2013Emden equations governing polytropic and isothermal gas spheres. New Astron. 17(6), 565\u2013569 (2012)","journal-title":"New Astron."},{"issue":"2","key":"2025_CR2","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.: Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J. Theor. Biol. 60(2), 449\u2013457 (1976)","journal-title":"J. Theor. Biol."},{"issue":"2","key":"2025_CR3","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.: The distribution of heat sources in the human head: A theoretical consideration. J. Theor. Biol. 54(2), 285\u2013287 (1975)","journal-title":"J. Theor. Biol."},{"key":"2025_CR4","doi-asserted-by":"publisher","first-page":"361","DOI":"10.2528\/PIER07090403","volume":"78","author":"M Dehghan","year":"2008","unstructured":"Dehghan, M., Shakeri, F.: Solution of an integro-differential equation arising in oscillating magnetic fields using He\u2019s homotopy perturbation method. Prog. Electromagn. Res. 78, 361\u2013376 (2008)","journal-title":"Prog. Electromagn. Res."},{"issue":"2","key":"2025_CR5","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/S0010-4655(03)00226-1","volume":"153","author":"JI Ramos","year":"2003","unstructured":"Ramos, J.I.: Linearization methods in classical and quantum mechanics. Comput. Phys. Commun. 153(2), 199\u2013208 (2003)","journal-title":"Comput. Phys. Commun."},{"issue":"6","key":"2025_CR6","first-page":"507","volume":"100","author":"A-M Wazwaz","year":"2014","unstructured":"Wazwaz, A.-M., Rach, R., Bougoffa, L., Duan, J.-S.: Solving the Lane\u2013Emden\u2013Fowler type equations of higher orders by the Adomian decomposition method. Comput. Model. Eng. Sci. 100(6), 507\u2013529 (2014)","journal-title":"Comput. Model. Eng. Sci."},{"issue":"1","key":"2025_CR7","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.apnum.2023.01.006","volume":"186","author":"J Shahni","year":"2023","unstructured":"Shahni, J., Singh, R., Cattani, C.: Bernoulli collocation method for the third-order Lane-Emden-Fowler boundary value problem. Appl. Numer. Math. 186(1), 100\u2013103 (2023)","journal-title":"Appl. Numer. Math."},{"key":"2025_CR8","doi-asserted-by":"publisher","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":"2025_CR9","unstructured":"Emden, R.: Gaskugeln: Anwendungen der mechanischen W\u00e4rmetheorie auf kosmologische und meteorologische Probleme, B. Teubner., (1907)"},{"issue":"16","key":"2025_CR10","doi-asserted-by":"publisher","first-page":"2243","DOI":"10.1002\/mma.2755","volume":"36","author":"M Lakestani","year":"2013","unstructured":"Lakestani, M., Dehghan, M.: Four techniques based on the b-spline expansion and the collocation approach for the numerical solution of the Lane\u2013Emden equation. Math. Methods Appl. Sci. 36(16), 2243\u20132253 (2013)","journal-title":"Math. Methods Appl. Sci."},{"key":"2025_CR11","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.matcom.2023.08.037","volume":"216","author":"N Sriwastav","year":"2024","unstructured":"Sriwastav, N., Barnwal, A.K., Ramos, H., Agarwal, R.P., Singh, M.: Advanced numerical scheme and its convergence analysis for a class of two-point singular boundary value problems. Math. Comput. Simul. 216, 30\u201348 (2024)","journal-title":"Math. Comput. Simul."},{"issue":"4","key":"2025_CR12","first-page":"2162","volume":"13","author":"N Sriwastav","year":"2023","unstructured":"Sriwastav, N., Barnwal, A.K., Ramos Calle, H., Agarwal, R.P., Singh, M., et al.: New approch based on collocation and shifted Chebyshev polynomials for a class of three-point singular BVPS. J. Appl. Anal. Comput. 13(4), 2162\u20132183 (2023)","journal-title":"J. Appl. Anal. Comput."},{"key":"2025_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2023.101976","volume":"67","author":"N Sriwastav","year":"2023","unstructured":"Sriwastav, N., Barnwal, A.K., Wazwaz, A.-M., Singh, M.: A novel numerical approach and stability analysis for a class of pantograph delay differential equation. J. Comput. Sci. 67, 101976 (2023)","journal-title":"J. Comput. Sci."},{"issue":"4","key":"2025_CR14","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.: An efficient numerical technique for the solution of nonlinear singular boundary value problems. Comput. Phys. Commun. 185(4), 1282\u20131289 (2014)","journal-title":"Comput. Phys. Commun."},{"issue":"1","key":"2025_CR15","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1186\/s13662-016-0754-1","volume":"2016","author":"F Zhou","year":"2016","unstructured":"Zhou, F., Xu, X.: Numerical solutions for the linear and nonlinear singular boundary value problems using laguerre wavelets. Adv. Diff. Equ. 2016(1), 17 (2016)","journal-title":"Adv. Diff. Equ."},{"issue":"7","key":"2025_CR16","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1140\/epjp\/i2016-16228-x","volume":"131","author":"K Parand","year":"2016","unstructured":"Parand, K., Yousefi, H., Delkhosh, M., Ghaderi, A.: A novel numerical technique to obtain an accurate solution to the thomas-fermi equation. Eur. Phys. J. Plus 131(7), 228 (2016)","journal-title":"Eur. Phys. J. Plus"},{"issue":"03","key":"2025_CR17","doi-asserted-by":"publisher","first-page":"1950005","DOI":"10.1142\/S021969131950005X","volume":"17","author":"AK Verma","year":"2019","unstructured":"Verma, A.K., Tiwari, D.: Higher resolution methods based on quasilinearization and Haar wavelets on Lane\u2013Emden equations. Int. J. Wavelets Multiresolution Inf. Process. 17(03), 1950005 (2019)","journal-title":"Int. J. Wavelets Multiresolution Inf. Process."},{"key":"2025_CR18","doi-asserted-by":"publisher","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\u2013Fowler type equations. Math. Comput. Simul. 174, 123\u2013133 (2020)","journal-title":"Math. Comput. Simul."},{"issue":"4","key":"2025_CR19","doi-asserted-by":"publisher","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."},{"issue":"6","key":"2025_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-021-01591-7","volume":"40","author":"MP Alam","year":"2021","unstructured":"Alam, M.P., Begum, T., Khan, A.: A high-order numerical algorithm for solving Lane\u2013Emden equations with various types of boundary conditions. Comput. Appl. Math. 40(6), 1\u201328 (2021)","journal-title":"Comput. Appl. Math."},{"key":"2025_CR21","doi-asserted-by":"publisher","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. J. Comput. Sci. 70, 102041 (2023)","journal-title":"J. Comput. Sci."},{"issue":"5","key":"2025_CR22","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1140\/epjp\/s13360-020-00424-6","volume":"135","author":"Z Sabir","year":"2020","unstructured":"Sabir, Z., Raja, M.A.Z., Umar, M., Shoaib, M.: Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden\u2013Fowler equation. Eur. Phys. J. Plus 135(5), 410 (2020)","journal-title":"Eur. Phys. J. Plus"},{"key":"2025_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2020\/7359242","volume":"2020","author":"JL Guirao","year":"2020","unstructured":"Guirao, J.L., Sabir, Z., Saeed, T.: Design and numerical solutions of a novel third-order nonlinear Emden\u2013Fowler delay differential model. Math. Probl. Eng. 2020, 1\u20139 (2020)","journal-title":"Math. Probl. Eng."},{"key":"2025_CR24","first-page":"319","volume":"331","author":"MK Iqbal","year":"2018","unstructured":"Iqbal, M.K., Abbas, M., Wasim, I.: New cubic B-spline approximation for solving third order Emden\u2013Flower type equations. Appl. Math. Comput. 331, 319\u2013333 (2018)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"2025_CR25","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1090\/qam\/910465","volume":"45","author":"C Chan","year":"1987","unstructured":"Chan, C., Hon, Y.: A constructive solution for a generalized Thomas-Fermi theory of ionized atoms. Q. Appl. Math. 45(3), 591\u2013599 (1987)","journal-title":"Q. Appl. Math."},{"key":"2025_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2024.102243","volume":"77","author":"J Shahni","year":"2024","unstructured":"Shahni, J., Singh, R.: A novel collocation approach using Chebyshev wavelets for solving fourth-order Emden-Fowler type equations. J. Comput. Sci. 77, 102243 (2024)","journal-title":"J. Comput. Sci."},{"issue":"12","key":"2025_CR27","doi-asserted-by":"publisher","first-page":"1093","DOI":"10.1515\/zna-2010-1213","volume":"65","author":"W Kim","year":"2010","unstructured":"Kim, W., Chun, C.: A modified Adomian decomposition method for solving higher-order singular boundary value problems. Zeitschrift f\u00fcr Naturforschung A 65(12), 1093\u20131100 (2010)","journal-title":"Zeitschrift f\u00fcr Naturforschung A"},{"key":"2025_CR28","doi-asserted-by":"crossref","unstructured":"Wazwaz, A.-M., Rach, R., Duan, J.-S.: Solving new fourth\u2013order Emden\u2013Fowler-type equations by the Adomian decomposition method. Int. J. Comput. Methods Eng. Sci. Mech. 16(2), 121\u2013131 (2015)","DOI":"10.1080\/15502287.2015.1009582"},{"key":"2025_CR29","doi-asserted-by":"crossref","unstructured":"Mazraeh, H.D., Parand, K.: GEPINN: An innovative hybrid method for a symbolic solution to the Lane-Emden type equation based on grammatical evolution and physics-informed neural networks. Astron. Comput. 100846 (2024)","DOI":"10.1016\/j.ascom.2024.100846"},{"key":"2025_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2024.109733","volume":"142","author":"HD Mazraeh","year":"2025","unstructured":"Mazraeh, H.D., Parand, K.: An innovative combination of deep Q-networks and context-free grammars for symbolic solutions to differential equations. Eng. Appl. Artif. Intell. 142, 109733 (2025)","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"1","key":"2025_CR31","doi-asserted-by":"publisher","first-page":"28797","DOI":"10.1038\/s41598-024-78907-0","volume":"14","author":"HD Mazraeh","year":"2024","unstructured":"Mazraeh, H.D., Parand, K., Hosseinzadeh, M., Lansky, J., Nul\u00ed\u010dek, V.: An improved water strider algorithm for solving the inverse burgers huxley equation. Sci. Rep. 14(1), 28797 (2024)","journal-title":"Sci. Rep."},{"issue":"4","key":"2025_CR32","first-page":"513","volume":"60","author":"M Bolhassani","year":"2024","unstructured":"Bolhassani, M., Dana Mazraeh, H., Parand, K.: A new method based on least-squares support vector regression for solving optimal control problems. Kybernetika 60(4), 513\u2013534 (2024)","journal-title":"Kybernetika"},{"issue":"3","key":"2025_CR33","first-page":"681","volume":"14","author":"H Dana Mazraeh","year":"2024","unstructured":"Dana Mazraeh, H., Parand, K., Farahani, H., Kheradpisheh, S.R.: An improved imperialist competitive algorithm for solving an inverse form of the Huxley equation. Iranian J. Numer. Anal. Optim. 14(3), 681\u2013707 (2024)","journal-title":"Iranian J. Numer. Anal. Optim."},{"key":"2025_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-018-1529-7","volume":"2018","author":"A Dezhbord","year":"2018","unstructured":"Dezhbord, A., Lotfi, T., Mahdiani, K.: A numerical approach for solving the high-order nonlinear singular Emden\u2013Fowler type equations. Adv. Diff. Equ. 2018, 1\u201317 (2018)","journal-title":"Adv. Diff. Equ."},{"key":"2025_CR35","doi-asserted-by":"crossref","unstructured":"Sahoo, N., Singh, R., Ramos, H.: An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems. Numer. Algoritm. 1\u201329 (2024)","DOI":"10.1007\/s11075-024-01882-0"},{"key":"2025_CR36","doi-asserted-by":"crossref","unstructured":"Parand, K., Delkhosh, M.: An effective numerical method for solving the nonlinear singular Lane-Emden type equations of various orders. J. Teknologi 79(1) (2025)","DOI":"10.11113\/jt.v79.8737"},{"issue":"1","key":"2025_CR37","first-page":"11","volume":"2","author":"N Singh","year":"2011","unstructured":"Singh, N., Kumar, M.: Adomian decomposition method for solving higher order boundary value problems. Math. Theory Model. 2(1), 11\u201322 (2011)","journal-title":"Math. Theory Model."},{"issue":"4","key":"2025_CR38","doi-asserted-by":"publisher","first-page":"321","DOI":"10.12732\/ijpam.v84i4.2","volume":"84","author":"K Aruna","year":"2013","unstructured":"Aruna, K., Kanth, A.R.: A novel approach for a class of higher order nonlinear singular boundary value problems. Int. J. Pure Appl. Math. 84(4), 321\u2013329 (2013)","journal-title":"Int. J. Pure Appl. Math."},{"key":"2025_CR39","doi-asserted-by":"publisher","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":"07","key":"2025_CR40","doi-asserted-by":"publisher","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. Int. J. Theor. Appl. Finan. 6(07), 767\u2013789 (2003)","journal-title":"Int. J. Theor. Appl. Finan."},{"issue":"1","key":"2025_CR41","doi-asserted-by":"publisher","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."},{"issue":"9","key":"2025_CR42","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\u2013Stokes equations. Appl. Math. Comput. 215(9), 3201\u20133213 (2010)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2025_CR43","doi-asserted-by":"publisher","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":"2025_CR44","doi-asserted-by":"crossref","unstructured":"Sahoo, N., Singh, R.: A stable higher-order numerical method for solving a system of third-order singular Emden-Fowler type equations. J. Appl. Math. Comput. 1\u201328 (2024)","DOI":"10.1007\/s12190-024-02233-x"},{"key":"2025_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2024.102474","volume":"83","author":"N Sahoo","year":"2024","unstructured":"Sahoo, N., Singh, R., Kanaujiya, A., Cattani, C.: A new fourth-order compact finite difference method for solving Lane-Emden-Fowler type singular boundary value problems. J. Comput. Sci. 83, 102474 (2024)","journal-title":"J. Comput. Sci."},{"key":"2025_CR46","doi-asserted-by":"crossref","unstructured":"Sahoo, N., Singh, R.: An efficient 6th-order compact difference scheme with error estimation for nonlocal Lane-Emden equation. J. Comput. Sci. 102529 (2025)","DOI":"10.1016\/j.jocs.2025.102529"},{"key":"2025_CR47","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":"2025_CR48","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. Int. J. Comput. Math. (2022) 1\u201319","DOI":"10.1080\/00207160.2022.2140278"},{"issue":"8","key":"2025_CR49","doi-asserted-by":"publisher","first-page":"3261","DOI":"10.1016\/j.cnsns.2008.12.015","volume":"14","author":"YQ Hasan","year":"2009","unstructured":"Hasan, Y.Q., Zhu, L.M.: A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations. Commun. Nonlinear Sci. Numer. Simul. 14(8), 3261\u20133265 (2009)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"6","key":"2025_CR50","doi-asserted-by":"publisher","first-page":"2592","DOI":"10.1016\/j.cnsns.2008.09.027","volume":"14","author":"YQ Hasan","year":"2009","unstructured":"Hasan, Y.Q., Zhu, L.M.: Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method. Commun. Nonlinear Sci. Numer. Simul. 14(6), 2592\u20132596 (2009)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2025_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112919","volume":"166","author":"M Shirzadi","year":"2023","unstructured":"Shirzadi, M., Rostami, M., Dehghan, M., Li, X.: American options pricing under regime-switching jump-diffusion models with meshfree finite point method. Chaos, Solitons Fractals 166, 112919 (2023)","journal-title":"Chaos, Solitons Fractals"},{"issue":"1","key":"2025_CR52","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1002\/num.22520","volume":"37","author":"M Shirzadi","year":"2021","unstructured":"Shirzadi, M., Dehghan, M., Bastani, A.F.: Optimal uniform error estimates for moving least-squares collocation with application to option pricing under jump-diffusion processes. Numer. Methods Partial Diff. Equ. 37(1), 98\u2013117 (2021)","journal-title":"Numer. Methods Partial Diff. Equ."},{"key":"2025_CR53","unstructured":"Godunov, S.K., Ryabenkii, V.S.: Difference Schemes: An Introduction to the Underlying Theory, Elsevier (1987)"},{"issue":"9","key":"2025_CR54","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/s13360-020-00780-3","volume":"135","author":"A Verma","year":"2020","unstructured":"Verma, A., Kumar, M.: Numerical solution of third-order Emden-Fowler type equations using artificial neural network technique. Eur. Phys. J. Plus 135(9), 1\u201314 (2020)","journal-title":"Eur. Phys. J. Plus"},{"issue":"1","key":"2025_CR55","first-page":"18","volume":"3","author":"H Mishra","year":"2015","unstructured":"Mishra, H., Saini, S.: Quartic B-spline method for solving singularly perturbed third-order boundary value problems. Am. J. Numer. Anal. 3(1), 18\u201324 (2015)","journal-title":"Am. J. Numer. Anal."},{"key":"2025_CR56","doi-asserted-by":"crossref","unstructured":"Rihan, F.A.: Continuous Runge\u2013Kutta schemes for pantograph type delay differential equations. Partial Diff. Equ. Appl. Math. 11, 100797 (2024)","DOI":"10.1016\/j.padiff.2024.100797"},{"issue":"3","key":"2025_CR57","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1515\/ijnsns-2021-0092","volume":"24","author":"R Gupta","year":"2023","unstructured":"Gupta, R., Kumar, S.: Numerical simulation of variable-order fractional differential equation of nonlinear Lane\u2013Emden type appearing in astrophysics. Int. J. Nonlinear Sci. Numer. Simul. 24(3), 965\u2013988 (2023)","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"2025_CR58","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.enganabound.2021.02.005","volume":"126","author":"M Shirzadi","year":"2021","unstructured":"Shirzadi, M., Dehghan, M., Bastani, A.F.: A trustable shape parameter in the kernel-based collocation method with application to pricing financial options. Eng. Anal. Bound. Elem. 126, 108\u2013117 (2021)","journal-title":"Eng. Anal. Bound. Elem."},{"key":"2025_CR59","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2020.106598","volume":"111","author":"M Shirzadi","year":"2021","unstructured":"Shirzadi, M., Dehghan, M.: Generalized regularized least-squares approximation of noisy data with application to stochastic PDEs. Appl. Math. Lett. 111, 106598 (2021)","journal-title":"Appl. Math. Lett."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02025-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-025-02025-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02025-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T09:02:43Z","timestamp":1770627763000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-025-02025-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,12]]},"references-count":59,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["2025"],"URL":"https:\/\/doi.org\/10.1007\/s11075-025-02025-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,12]]},"assertion":[{"value":"14 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2025","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 state that they have no conflicts of interest related to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}},{"value":"Not Applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}