{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:51:05Z","timestamp":1760143865286,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems.<\/jats:p>","DOI":"10.3390\/axioms13030165","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T11:19:24Z","timestamp":1709291964000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9210-8278","authenticated-orcid":false,"given":"Richard Olatokunbo","family":"Akinola","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Jos, Jos 930105, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2699-1490","authenticated-orcid":false,"given":"Ali","family":"Shokri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Maragheh, Maragheh 83111-55181, Iran"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6304-4965","authenticated-orcid":false,"given":"Joshua","family":"Sunday","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Jos, Jos 930105, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7938-063X","authenticated-orcid":false,"given":"Daniela","family":"Marian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Oyindamola D.","family":"Akinlabi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Jos, Jos 930105, Nigeria"}],"role":[{"role":"author","vocab":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0377-0427(93)90025-7","article-title":"Ill-conditioned matrices and the integration of stiff ODEs","volume":"48","author":"Shampine","year":"1993","journal-title":"J. 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