{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T10:08:57Z","timestamp":1776938937514,"version":"3.51.4"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,5,8]],"date-time":"2015-05-08T00:00:00Z","timestamp":1431043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this work we generate the numerical solutions of Burgers\u2019 equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers\u2019 equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.<\/jats:p>","DOI":"10.3390\/a8020224","type":"journal-article","created":{"date-parts":[[2015,5,8]],"date-time":"2015-05-08T10:56:41Z","timestamp":1431082601000},"page":"224-233","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Numerical Solution of Turbulence Problems by Solving Burgers\u2019 Equation"],"prefix":"10.3390","volume":"8","author":[{"given":"Alicia","family":"Cordero","sequence":"first","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Polytechnical University of Valencia, Camino de Vera, s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Franques","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Polytechnical University of Valencia, Camino de Vera, s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan","family":"Torregrosa","sequence":"additional","affiliation":[{"name":"Institute for Multidisciplinary Mathematics, Polytechnical University of Valencia, Camino de Vera, s\/n, 46022 Val\u00e8ncia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.jcp.2003.11.016","article-title":"A comparison of implicit time integration methods for nonlinear relaxation and diffusion","volume":"196","author":"Lowrie","year":"2004","journal-title":"J. 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