{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T12:06:26Z","timestamp":1772021186291,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T00:00:00Z","timestamp":1771977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2026"],"award-info":[{"award-number":["QU-APC-2026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Burgers\u2013Huxley equation is a nonlinear partial differential equation that incorporates convective, diffusive and reactive effects and arises in various reaction\u2013diffusion and fluid flow models. In this paper, a numerical method based on the method of lines is proposed for its solution. The spatial derivatives are approximated using a third-order finite difference scheme, which converts the governing partial differential equation into a system of ordinary differential equations. The resulting semi-discrete system is solved in time using the classical fourth-order Runge\u2013Kutta method. The stability and convergence properties of the proposed scheme are analyzed to establish its numerical reliability. Several numerical experiments are presented to illustrate the accuracy and efficiency of the method. The computed results confirm that the proposed approach provides accurate and stable solutions for the Burgers\u2013Huxley equation.<\/jats:p>","DOI":"10.3390\/axioms15030158","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T10:59:16Z","timestamp":1772017156000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Method of Lines Scheme with Third-Order Finite Differences for Burgers\u2013Huxley Equation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7999-2847","authenticated-orcid":false,"given":"Muhammad","family":"Yaseen","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Ameer","family":"Hamza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8309-6121","authenticated-orcid":false,"given":"Khidir Shaib","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naglaa","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1088\/0305-4470\/23\/3\/011","article-title":"Solitary wave solutions of the generalized Burgers\u2013Huxley equation","volume":"23","author":"Wang","year":"1990","journal-title":"J. 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