{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T11:18:01Z","timestamp":1710674281122},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T00:00:00Z","timestamp":1694044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"This paper introduces an efficient approach for solving Lane\u2013Emden\u2013Fowler problems. Our method utilizes two Nystr\u00f6m schemes to perform the integration. To overcome the singularity at the left end of the interval, we combine an optimized scheme of Nystr\u00f6m type with a set of Nystr\u00f6m formulas that are used at the fist subinterval. The optimized technique is obtained after imposing the vanishing of some of the local truncation errors, which results in a set of symmetric hybrid points. By solving an algebraic system of equations, our proposed approach generates simultaneous approximations at all grid points, resulting in a highly effective technique that outperforms several existing numerical methods in the literature. To assess the efficiency and accuracy of our approach, we perform some numerical tests on diverse real-world problems, including singular boundary value problems (SBVPs) from chemical kinetics.<\/jats:p>","DOI":"10.3390\/sym15091720","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T11:52:11Z","timestamp":1694173931000},"page":"1720","source":"Crossref","is-referenced-by-count":1,"title":["A Pair of Optimized Nystr\u00f6m Methods with Symmetric Hybrid Points for the Numerical Solution of Second-Order Singular Boundary Value Problems"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2791-6230","authenticated-orcid":false,"given":"Higinio","family":"Ramos","sequence":"first","affiliation":[{"name":"Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain"},{"name":"Department of Mathematics, Escuela Polit\u00e9cnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-1293-4719","authenticated-orcid":false,"given":"Mufutau Ajani","family":"Rufai","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0516-0033","authenticated-orcid":false,"given":"Bruno","family":"Carpentieri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0362-546X(93)90045-T","article-title":"Existence of solutions of a kind of singular boundary value problem","volume":"21","author":"Zhang","year":"1993","journal-title":"Nonlinear Anal. 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