{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T00:12:23Z","timestamp":1781914343616,"version":"3.54.5"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s40314-023-02468-7","type":"journal-article","created":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T14:02:17Z","timestamp":1696341737000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hybrid model for the optimal numerical solution of nonlinear ordinary differential systems"],"prefix":"10.1007","volume":"42","author":[{"given":"Narendra","family":"Kumar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Diksha","family":"Tiwari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8768-094X","authenticated-orcid":false,"given":"Amit K.","family":"Verma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,10,3]]},"reference":[{"issue":"4","key":"2468_CR1","doi-asserted-by":"crossref","first-page":"2391","DOI":"10.1016\/j.aej.2020.02.035","volume":"59","author":"T Abdeljawad","year":"2020","unstructured":"Abdeljawad T, Amin R, Shah K, Al-Mdallal Q, Jarad F (2020) Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method. Alexandria Eng J 59(4):2391\u20132400","journal-title":"Alexandria Eng J"},{"issue":"3","key":"2468_CR2","first-page":"505","volume":"8","author":"N Aghazadeh","year":"2020","unstructured":"Aghazadeh N, Ahmadnezhad G, Rezapour S (2020) Haar wavelet iteration method for solving time fractional Fisher\u2019s equation. Comput Methods Differ Equ 8(3):505\u201322","journal-title":"Comput Methods Differ Equ"},{"key":"2468_CR3","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1155\/2013\/259371","volume":"2013","author":"ES Alaidarous","year":"2013","unstructured":"Alaidarous ES, Ullah MZ, Ahmad F, Al-Fhaid AS (2013) An efficient higher-order quasilinearization method for solving nonlinear bvps. J Appl Math 2013:11","journal-title":"J Appl Math"},{"key":"2468_CR4","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2020.113028","volume":"381","author":"R Amin","year":"2021","unstructured":"Amin R, Shah K, Asif M, Khan I, Ullah F (2021) An efficient algorithm for numerical solution of fractional integro-differential equations via Haar wavelet. J Comput Appl Math 381:113028","journal-title":"J Comput Appl Math"},{"issue":"1","key":"2468_CR5","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.cam.2008.07.003","volume":"225","author":"E Babolian","year":"2009","unstructured":"Babolian E, Shahsavaran A (2009) Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets. J Comput Appl Math 225(1):87\u201395","journal-title":"J Comput Appl Math"},{"issue":"1\u20132","key":"2468_CR6","first-page":"301","volume":"62","author":"AK Barnwal","year":"2019","unstructured":"Barnwal AK, Pathak P (2019) Successive iteration technique for singular nonlinear system with four-point boundary conditions. J Appl Math Comput 62(1\u20132):301\u201324","journal-title":"J Appl Math Comput"},{"key":"2468_CR7","first-page":"212","volume-title":"Quasilinearization and non-linear boundary value problems","author":"RE Bellman","year":"1965","unstructured":"Bellman RE, Kalaba RE (1965) Quasilinearization and non-linear boundary value problems, vol 52. American Elsevier Publishing Company Inc., New York, pp 212\u2013212"},{"issue":"1","key":"2468_CR8","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1080\/09720502.2001.10700287","volume":"4","author":"C Carlo","year":"2001","unstructured":"Carlo C (2001) Haar wavelet splines. J Interdiscip Math 4(1):35\u201347","journal-title":"J Interdiscip Math"},{"issue":"1","key":"2468_CR9","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1049\/ip-cta:19970702","volume":"144","author":"CF Chen","year":"1997","unstructured":"Chen CF, Hsiao CH (1997) Haar wavelet method for solving lumped and distributed-parameter systems. IEE Proc Control Theory Appl 144(1):87\u201394","journal-title":"IEE Proc Control Theory Appl"},{"key":"2468_CR10","doi-asserted-by":"crossref","DOI":"10.1088\/1742-6596\/268\/1\/012006","volume":"268","author":"D Flockerzi","year":"2011","unstructured":"Flockerzi D, Sundmacher K (2011) On coupled Lane-Emden equations arising in dusty fluid models. J Phys Conf Ser 268:012006","journal-title":"J Phys Conf Ser"},{"issue":"9","key":"2468_CR11","doi-asserted-by":"crossref","first-page":"2691","DOI":"10.1007\/s10910-018-0912-7","volume":"56","author":"T Hao","year":"2018","unstructured":"Hao T, Cong F, Shang Y (2018) 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","journal-title":"J Math Chem"},{"issue":"8","key":"2468_CR12","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1007\/s10910-019-01048-7","volume":"57","author":"J He","year":"2019","unstructured":"He J, Ji F (2019) Taylor series solution for Lane-Emden equation. J Math Chem 57(8):1932\u20131934","journal-title":"J Math Chem"},{"key":"2468_CR13","first-page":"528","volume":"8","author":"M Heydari","year":"2022","unstructured":"Heydari M, Avazzadeh Z, Hosseinzadeh N (2022) Haar wavelet method for solving high-order differential equations with multi-point boundary conditions. J Appl Comput Mech 8:528\u2013544","journal-title":"J Appl Comput Mech"},{"issue":"5","key":"2468_CR14","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1016\/j.matcom.2003.11.011","volume":"64","author":"CH Hsiao","year":"2004","unstructured":"Hsiao CH (2004) Haar wavelet approach to linear stiff systems. Math Comput Simul 64(5):561\u2013567","journal-title":"Math Comput Simul"},{"issue":"6","key":"2468_CR15","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0378-4754(01)00275-0","volume":"57","author":"C-H Hsiao","year":"2001","unstructured":"Hsiao C-H, Wang W-J (2001) Haar wavelet approach to nonlinear stiff systems. Math Comput Simul 57(6):347\u2013353","journal-title":"Math Comput Simul"},{"issue":"9","key":"2468_CR16","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1016\/j.mcm.2010.06.023","volume":"52","author":"S Islam","year":"2010","unstructured":"Islam S, Aziz I, \u0160arler B (2010) The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets. Math Comput Model 52(9):1577\u20131590","journal-title":"Math Comput Model"},{"issue":"3","key":"2468_CR17","doi-asserted-by":"crossref","first-page":"176","DOI":"10.4236\/ajcm.2011.13020","volume":"1","author":"H Kaur","year":"2011","unstructured":"Kaur H, Mittal RC, Mishra V (2011) Haar wavelet quasilinearization approach for solving nonlinear boundary value problems. Am J Comput Math 1(3):176\u2013182","journal-title":"Am J Comput Math"},{"issue":"9","key":"2468_CR18","doi-asserted-by":"crossref","first-page":"2169","DOI":"10.1016\/j.cpc.2013.04.013","volume":"184","author":"H Kaur","year":"2013","unstructured":"Kaur H, Mittal RC, Mishra V (2013a) Haar wavelet approximate solutions for the generalized Lane-Emden equations arising in astrophysics. Comput Phys Commun 184(9):2169\u20132177","journal-title":"Comput Phys Commun"},{"key":"2468_CR19","unstructured":"Kaur H, Mittal RC, Mishra V (2013b) A collocation approach with uniform Haar wavelets to solve Volterra population model for population growth of a species. Math Sci Int Res J 2"},{"key":"2468_CR20","unstructured":"Kaur H, Mishra V, Mittal RC (2013c) Numerical solution of a laminar viscous flow boundary layer equation using uniform Haar wavelet quasi-linearization method. In: World Academy of Science, Engineering and Technology, p 79"},{"issue":"21","key":"2468_CR21","doi-asserted-by":"crossref","first-page":"4958","DOI":"10.1016\/j.apm.2014.03.019","volume":"38","author":"H Kaur","year":"2014","unstructured":"Kaur H, Mittal RC, Mishra V (2014) Haar wavelet solutions of nonlinear oscillator equations. Appl Math Model 38(21):4958\u20134971","journal-title":"Appl Math Model"},{"issue":"3","key":"2468_CR22","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1080\/09205071.2020.1713225","volume":"34","author":"A Kumar","year":"2020","unstructured":"Kumar A, Hashmi MS, Ansari AQ, Arzykulov S (2020) Haar wavelet based algorithm for solution of second order electromagnetic problems in time and space domains. J Electromagn Waves Appl 34(3):362\u2013374","journal-title":"J Electromagn Waves Appl"},{"key":"2468_CR23","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.matcom.2004.10.005","volume":"68","author":"U Lepik","year":"2005","unstructured":"Lepik U (2005) Numerical solution of differential equations using Haar wavelets. Math Comput Simul 68:127\u2013143","journal-title":"Math Comput Simul"},{"issue":"695\u2013704","key":"2468_CR24","first-page":"02","volume":"185","author":"U Lepik","year":"2007","unstructured":"Lepik U (2007) Numerical solution of evolution equations by the Haar wavelet method. Appl Math Comput 185(695\u2013704):02","journal-title":"Appl Math Comput"},{"key":"2468_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-04295-4","volume-title":"Haar wavelets with applications","author":"U Lepik","year":"2014","unstructured":"Lepik U, Hein H (2014) Haar wavelets with applications. Springer, Cham"},{"key":"2468_CR26","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1515\/wwfaa-2016-0003","volume":"2","author":"M Maarjus Kirs","year":"2016","unstructured":"Maarjus Kirs M, Mikola A, Haavajoe E, Ounapuu BS, Majak J (2016) Haar wavelet method for vibration analysis of nanobeams. Waves Wavelets Fract 2:20\u201328","journal-title":"Waves Wavelets Fract"},{"issue":"4","key":"2468_CR27","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1007\/s10910-019-01014-3","volume":"57","author":"M Mahalakshmi","year":"2019","unstructured":"Mahalakshmi M, Hariharan G (2019) An efficient wavelet-based method for the numerical solutions of nonlinear coupled reaction-diffusion equations in biochemical engineering. J Math Chem 57(4):1154\u20131168","journal-title":"J Math Chem"},{"key":"2468_CR28","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.compositesb.2015.06.008","volume":"80","author":"J Majak","year":"2015","unstructured":"Majak J, Shvartsman B, Karjust K, Mikola M, Haavaj A, Pohlak M (2015a) On the accuracy of the Haar wavelet discretization method. Compos B Eng 80:321\u2013327","journal-title":"Compos B Eng"},{"key":"2468_CR29","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.compstruct.2015.02.050","volume":"126","author":"J Majak","year":"2015","unstructured":"Majak J, Shvartsman BS, Kirs M, Pohlak M, Herranen H (2015b) Convergence theorem for the Haar wavelet based discretization method. Compos Struct 126:227\u2013232","journal-title":"Compos Struct"},{"key":"2468_CR30","volume":"25","author":"J Majak","year":"2020","unstructured":"Majak J, Shvartsman B, Ratas M, Bassir D, Pohlak M, Karjust K, Eerme M (2020) Higher-order Haar wavelet method for vibration analysis of nanobeams. Mater Today Commun 25:101290","journal-title":"Mater Today Commun"},{"issue":"7","key":"2468_CR31","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1016\/j.camwa.2018.11.018","volume":"77","author":"\u00d6 Oru\u00e7","year":"2019","unstructured":"Oru\u00e7 \u00d6 (2019) A non-uniform Haar wavelet method for numerically solving two-dimensional convection-dominated equations and two-dimensional near singular elliptic equations. Comput Math Appl 77(7):1799\u20131820","journal-title":"Comput Math Appl"},{"key":"2468_CR32","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1007\/s10910-015-0507-5","volume":"53","author":"\u00d6 Oru\u00e7","year":"2015","unstructured":"Oru\u00e7 \u00d6, Fatih B, Alaattin E (2015) A Haar wavelet finite difference hybrid method for the numerical solution of the modified Burgers\u2019 equation. J Math Chem 53:1592\u20131607","journal-title":"J Math Chem"},{"key":"2468_CR33","doi-asserted-by":"crossref","first-page":"3235","DOI":"10.1007\/s00009-016-0682-z","volume":"13","author":"\u00d6 Oru\u00e7","year":"2016","unstructured":"Oru\u00e7 \u00d6, Fatih B, Alaattin E (2016) Numerical solutions of regularized long wave equation by Haar wavelet method. Mediterr J Math 13:3235\u20133253","journal-title":"Mediterr J Math"},{"key":"2468_CR34","doi-asserted-by":"crossref","first-page":"195","DOI":"10.11121\/ijocta.01.2017.00396","volume":"7","author":"\u00d6 Oru\u00e7","year":"2017","unstructured":"Oru\u00e7 \u00d6, Bulut F, Esen A (2017) A numerical treatment based on Haar wavelets for coupled KdV equation. Int J Optimiz Control Theor Appl (IJOCTA) 7:195\u2013204","journal-title":"Int J Optimiz Control Theor Appl (IJOCTA)"},{"key":"2468_CR35","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s00366-018-0584-8","volume":"35","author":"\u00d6 Oru\u00e7","year":"2019","unstructured":"Oru\u00e7 \u00d6, Esen A, Bulut F (2019) A Haar wavelet approximation for two-dimensional time fractional reaction-subdiffusion equation. Eng Comput 35:75\u201386","journal-title":"Eng Comput"},{"issue":"1","key":"2468_CR36","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1515\/nleng-2018-0062","volume":"8","author":"Y Ozturk","year":"2018","unstructured":"Ozturk Y (2018) An efficient numerical algorithm for solving system of Lane-Emden type equations arising in engineering. Nonlinear Eng 8(1):429\u2013437","journal-title":"Nonlinear Eng"},{"issue":"11","key":"2468_CR37","doi-asserted-by":"crossref","first-page":"3860","DOI":"10.1016\/j.amc.2009.11.029","volume":"215","author":"RK Pandey","year":"2010","unstructured":"Pandey RK, Verma AK (2010a) Monotone method for singular bvp in the presence of upper and lower solutions. Appl Math Comput 215(11):3860\u20133867","journal-title":"Appl Math Comput"},{"issue":"1","key":"2468_CR38","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s12190-009-0299-5","volume":"33","author":"RK Pandey","year":"2010","unstructured":"Pandey RK, Verma AK (2010b) On solvability of derivative dependent doubly singular boundary value problems. J Appl Math Comput 33(1):489\u2013511","journal-title":"J Appl Math Comput"},{"key":"2468_CR39","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2019.123738","volume":"545","author":"N Pervaiz","year":"2020","unstructured":"Pervaiz N, Aziz I (2020) Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations. Phys A 545:123738","journal-title":"Phys A"},{"key":"2468_CR40","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, Wazwaz A (2014) Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J Math Chem 52:255\u2013267","journal-title":"J Math Chem"},{"issue":"3","key":"2468_CR41","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1016\/j.apm.2011.07.045","volume":"36","author":"M Rehman","year":"2012","unstructured":"Rehman M, Khan RA (2012) A numerical method for solving boundary value problems for fractional differential equations. Appl Math Model 36(3):894\u2013907","journal-title":"Appl Math Model"},{"issue":"6","key":"2468_CR42","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/S0362-546X(99)00152-2","volume":"42","author":"M Ruyun","year":"2000","unstructured":"Ruyun M (2000) Multiple nonnegative solutions of second-order systems of boundary value problems. Nonlinear Anal Theory Methods Appl 42(6):1003\u20131010","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"2468_CR43","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s40819-020-00836-z","volume":"6","author":"R Singh","year":"2020","unstructured":"Singh R (2020) Solving coupled Lane-Emden equations by Green\u2019s function and decomposition technique. Int J Appl Comput Math 6:80","journal-title":"Int J Appl Comput Math"},{"issue":"4","key":"2468_CR44","first-page":"513","volume":"21","author":"M Singh","year":"2017","unstructured":"Singh M, Verma AK (2017) Nonlinear three point singular bvps: a classification. Commun Appl Anal 21(4):513\u2013532","journal-title":"Commun Appl Anal"},{"key":"2468_CR45","first-page":"785","volume":"81","author":"R Singh","year":"2019","unstructured":"Singh R, Wazwaz AM (2019) An efficient algorithm for solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions: the homotopy analysis method. MATCH Commun Math Comput Chem 81:785\u2013800","journal-title":"MATCH Commun Math Comput Chem"},{"issue":"1","key":"2468_CR46","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s12190-014-0773-6","volume":"47","author":"M Singh","year":"2015","unstructured":"Singh M, Verma AK, Agarwal RP (2015) Maximum and anti-maximum principles for three point sbvps and nonlinear three point sbvps. J Appl Math Comput 47(1):249\u2013263","journal-title":"J Appl Math Comput"},{"key":"2468_CR47","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 (2019a) Haar wavelet collocation method for Lane-Emden equations with Dirichlet, Neumann and Neumann-Robin boundary conditions. J Comput Appl Math 346:150\u2013161","journal-title":"J Comput Appl Math"},{"issue":"11","key":"2468_CR48","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1140\/epjp\/i2019-12889-1","volume":"134","author":"R Singh","year":"2019","unstructured":"Singh R, Shahni J, Garg H, Garg A (2019b) Haar wavelet collocation approach for Lane-Emden equations arising in mathematical physics and astrophysics. Eur Phys J Plus 134(11):548","journal-title":"Eur Phys J Plus"},{"key":"2468_CR49","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 (2020) Haar wavelet quasilinearization method for numerical solution of Emden-Fowler type equations. Math Comput Simul 174:123\u2013133","journal-title":"Math Comput Simul"},{"key":"2468_CR50","doi-asserted-by":"crossref","unstructured":"Swati KS, Verma AK, Singh M (2020) Higher order Emden-Fowler type equations via uniform Haar wavelet resolution technique. J Comput Appl Math 376:112836","DOI":"10.1016\/j.cam.2020.112836"},{"key":"2468_CR51","doi-asserted-by":"crossref","first-page":"3024","DOI":"10.1021\/ie060860+","volume":"46","author":"S Talwalkar","year":"2007","unstructured":"Talwalkar S, Mankar S, Katariya A, Aghalayam P, Ivanova M, Sundmacher K, Mahajani S (2007) Selectivity engineering with reactive distillation for dimerization of c4 olefins: experimental and theoretical studies. Ind Eng Chem Res 46:3024\u20133034","journal-title":"Ind Eng Chem Res"},{"issue":"14","key":"2468_CR52","doi-asserted-by":"crossref","first-page":"4709","DOI":"10.1016\/j.na.2011.04.037","volume":"74","author":"AK Verma","year":"2011","unstructured":"Verma AK (2011) The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent bvp in the presence of upper and lower solutions. Nonlinear Anal Theory Methods Appl 74(14):4709\u20134717","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"173","key":"2468_CR53","first-page":"1","volume":"2014","author":"AK Verma","year":"2014","unstructured":"Verma AK, Singh M (2014) Existence of solutions for three-point bvps arising in bridge design. Electron J Differ Equ 2014(173):1\u201311","journal-title":"Electron J Differ Equ"},{"issue":"4","key":"2468_CR54","doi-asserted-by":"crossref","first-page":"457","DOI":"10.3846\/13926292.2015.1065293","volume":"20","author":"AK Verma","year":"2015","unstructured":"Verma AK, Singh M (2015a) A note on existence results for a class of three-point nonlinear bvps. Math Model Anal 20(4):457\u2013470","journal-title":"Math Model Anal"},{"issue":"2","key":"2468_CR55","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1007\/s10910-014-0447-5","volume":"53","author":"AK Verma","year":"2015","unstructured":"Verma AK, Singh M (2015b) Singular nonlinear three point bvps arising in thermal explosion in a cylindrical reactor. J Math Chem 53(2):670\u2013684","journal-title":"J Math Chem"},{"issue":"03","key":"2468_CR56","doi-asserted-by":"crossref","first-page":"1950005","DOI":"10.1142\/S021969131950005X","volume":"17","author":"AK Verma","year":"2019","unstructured":"Verma AK, Tiwari D (2019a) Higher resolution methods based on quasilinearization and Haar wavelets on Lane-Emden equations. Int J Wavelets Multiresol Inf Process 17(03):1950005","journal-title":"Int J Wavelets Multiresol Inf Process"},{"key":"2468_CR57","unstructured":"Verma AK, Tiwari D (2019b) A note on Legendre, Hermite, Chebyshev, Laguerre and Gegenbauer wavelets with an application on sbvps arising in real life. arXiv"},{"key":"2468_CR58","unstructured":"Verma AK, Tiwari D (2019c) On some computational aspects of Hermite wavelets on a class of sbvps arising in exothermic reactions. arXiv"},{"issue":"7","key":"2468_CR59","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.3390\/math8071045","volume":"8","author":"AK Verma","year":"2020","unstructured":"Verma AK, Pandit B, Verma L, Agarwal RP (2020a) A review on a class of second order nonlinear singular BVPs. Mathematics 8(7):1045","journal-title":"Mathematics"},{"issue":"2","key":"2468_CR60","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1108\/EC-04-2020-0181","volume":"38","author":"AK Verma","year":"2020","unstructured":"Verma AK, Kumar N, Tiwari D (2020b) Haar wavelets collocation method for a system of nonlinear singular differential equations. Eng Comput 38(2):659\u201398","journal-title":"Eng Comput"},{"issue":"9","key":"2468_CR61","doi-asserted-by":"crossref","first-page":"1950066","DOI":"10.1142\/S021987621950066X","volume":"17","author":"AK Verma","year":"2020","unstructured":"Verma AK, Urus N, Singh M (2020c) Monotone iterative technique for a class of four point bvps with reversed ordered upper and lower solutions. Int J Comput Methods 17(9):1950066","journal-title":"Int J Comput Methods"},{"key":"2468_CR62","unstructured":"Verma L, Pandit B, Verma AK (2020d) Taylor series solution of some real life problems: Odes and pdes. Preprint"},{"issue":"1","key":"2468_CR63","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1002\/mma.2776","volume":"37","author":"AM Wazwaz","year":"2014","unstructured":"Wazwaz AM, Rach R, Duan J (2014) A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method. Math Methods Appl Sci 37(1):10\u201319","journal-title":"Math Methods Appl Sci"},{"issue":"4","key":"2468_CR64","doi-asserted-by":"crossref","first-page":"377","DOI":"10.3390\/math7040377","volume":"7","author":"L Xie","year":"2019","unstructured":"Xie L, Zhou C, Xu S (2019) Solving the systems of equations of Lane-Emden type by differential transform method coupled with Adomian polynomials. Mathematics 7(4):377","journal-title":"Mathematics"},{"issue":"1","key":"2468_CR65","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s12190-008-0133-5","volume":"29","author":"H Zhang","year":"2009","unstructured":"Zhang H, Sun J (2009) Existence of positive solution to singular systems of second-order four-point bvps. J Appl Math Comput 29(1):325\u2013339","journal-title":"J Appl Math Comput"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02468-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02468-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02468-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T11:24:30Z","timestamp":1702034670000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02468-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,3]]},"references-count":65,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["2468"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02468-7","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,3]]},"assertion":[{"value":"16 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 September 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"322"}}