{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T00:12:30Z","timestamp":1781914350891,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T00:00:00Z","timestamp":1650326400000},"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":"<jats:p>A dependable semi-analytical method via the application of a modified Adomian Decomposition Method (ADM) to tackle the coupled system of Emden\u2013Fowler-type equations has been proposed. More precisely, an effective differential operator together with its corresponding inverse is successfully constructed. Moreover, this operator is able to navigate to the closed-form solution easily without resorting to converting the coupled system to a system of Volterra integral equations; as in the case of a well-known reference in the literature. Lastly, the effectiveness of the method is demonstrated on some coupled systems of the governing model, and a speedier convergence rate was noted.<\/jats:p>","DOI":"10.3390\/sym14050843","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:22:43Z","timestamp":1650414163000},"page":"843","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Method for the Solution of Coupled System of Emden\u2013Fowler\u2013Type Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Aishah A.","family":"Alsulami","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 80327, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mariam","family":"AL-Mazmumy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 80327, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huda O.","family":"Bakodah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 80327, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nawal","family":"Alzaid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 80327, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,19]]},"reference":[{"key":"ref_1","first-page":"45","article-title":"A new method for solving singular initial value problems in the second-order ordinary differential equations","volume":"128","author":"Wazwaz","year":"2002","journal-title":"Appl. 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