{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:08:35Z","timestamp":1760242115362,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,24]],"date-time":"2018-12-24T00:00:00Z","timestamp":1545609600000},"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>We calculated Noether-like operators and first integrals of a scalar second-order ordinary differential equation using the complex Lie-symmetry method. We numerically integrated the equations using a symplectic Runge\u2013Kutta method. It was seen that these structure-preserving numerical methods provide qualitatively correct numerical results, and good preservation of first integrals is obtained.<\/jats:p>","DOI":"10.3390\/sym11010011","type":"journal-article","created":{"date-parts":[[2018,12,24]],"date-time":"2018-12-24T10:37:49Z","timestamp":1545647869000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Complex Lie-Symmetry Approach to Calculate First Integrals and Their Numerical Preservation"],"prefix":"10.3390","volume":"11","author":[{"given":"Wajeeha","family":"Irshad","sequence":"first","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1709-1159","authenticated-orcid":false,"given":"Yousaf","family":"Habib","sequence":"additional","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan"},{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}]},{"given":"Muhammad Umar","family":"Farooq","sequence":"additional","affiliation":[{"name":"Department of BS and H, College of E and ME, National University of Sciences and Technology, Peshawar Road, Rawalpindi 46000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,24]]},"reference":[{"key":"ref_1","unstructured":"Ibragimov, N.H. (1999). Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley and Sons."},{"key":"ref_2","unstructured":"Lie, S. (1888). Theorie der Transformationsgruppen, Teubner."},{"key":"ref_3","unstructured":"Lie, S. (1891). Vorlesungen \u00fcber Differentialgleichungen Mit Bekannten Infinitesimalen Transformationen, Teubner."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Stephani, H. (1989). 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