{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T03:14:33Z","timestamp":1771038873231,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T00:00:00Z","timestamp":1571788800000},"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 article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers\u2019 equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature.<\/jats:p>","DOI":"10.3390\/axioms8040119","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T03:20:36Z","timestamp":1571973636000},"page":"119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":61,"title":["Numerical Solutions of Coupled Burgers\u2019 Equations"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5438-5407","authenticated-orcid":false,"given":"Hijaz","family":"Ahmad","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tufail A.","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, 39, 00186 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"412","DOI":"10.2478\/cmam-2009-0026","article-title":"A Fourier Pseudospectral Method for Solving Coupled Viscous Burgers Equations","volume":"9","author":"Rashid","year":"2009","journal-title":"Comput. 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