{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T07:27:20Z","timestamp":1772263640046,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT, the Thailand Science Research and Innovation (TSRI) Basic Research Fund","award":["FRB650048\/0164"],"award-info":[{"award-number":["FRB650048\/0164"]}]},{"name":"The Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT, the Thailand Science Research and Innovation (TSRI) Basic Research Fund","award":["15\/2562"],"award-info":[{"award-number":["15\/2562"]}]},{"name":"Petchra Pra Jom Klao PhD Research Scholarship from KMUTT","award":["FRB650048\/0164"],"award-info":[{"award-number":["FRB650048\/0164"]}]},{"name":"Petchra Pra Jom Klao PhD Research Scholarship from KMUTT","award":["15\/2562"],"award-info":[{"award-number":["15\/2562"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, a new pair of diagonally implicit Runge\u2013Kutta\u2013Nystr\u00f6m methods with four stages is constructed. The proposed method has been derived to solve initial value problems of special second-order ordinary-differential equations. The principal local truncation error of the new method is obtained, and the main characteristics of the new method are analyzed. Some numerical experiments are performed, which demonstrate the robustness and efficiency of the new embedded pair.<\/jats:p>","DOI":"10.3390\/axioms11100565","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T21:18:02Z","timestamp":1666127882000},"page":"565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Development of an Efficient Diagonally Implicit Runge\u2013Kutta\u2013Nystr\u00f6m 5(4) Pair for Special Second Order IVPs"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7169-1580","authenticated-orcid":false,"given":"Musa Ahmed","family":"Demba","sequence":"first","affiliation":[{"name":"KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand"},{"name":"Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand"},{"name":"Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, Wudil P.M.B 3244, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8614-8281","authenticated-orcid":false,"given":"Norazak","family":"Senu","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2791-6230","authenticated-orcid":false,"given":"Higinio","family":"Ramos","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Sciences, University of Salamanca, 37008 Salamanca, Spain"},{"name":"Escuela Polit\u00e9cnica Superior, Avda. de Requejo, 33, 49022 Zamora, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1435-3854","authenticated-orcid":false,"given":"Wiboonsak","family":"Watthayu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/0377-0427(87)90208-1","article-title":"A note on a diagonally implicit Runge\u2013Kutta\u2013Nystr\u00f6m method","volume":"19","author":"Sommeijer","year":"1987","journal-title":"J. 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