{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:43:20Z","timestamp":1776797000643,"version":"3.51.2"},"reference-count":0,"publisher":"American Mathematical Society (AMS)","issue":"287","license":[{"start":{"date-parts":[[2014,8,5]],"date-time":"2014-08-05T00:00:00Z","timestamp":1407196800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We consider a nonlocal scalar conservation law proposed by Andrew C. Fowler to describe the dynamics of dunes, and we develop a numerical procedure based on splitting methods to approximate its solutions. We begin by proving the convergence of the well-known Lie formula, which is an approximation of the exact solution of order one in time. We next use the split-step Fourier method to approximate the continuous problem using the fast Fourier transform and the finite difference method. Our numerical experiments confirm the theoretical results.<\/p>","DOI":"10.1090\/s0025-5718-2013-02757-3","type":"journal-article","created":{"date-parts":[[2013,8,8]],"date-time":"2013-08-08T13:46:05Z","timestamp":1375969565000},"page":"1121-1141","source":"Crossref","is-referenced-by-count":5,"title":["Splitting methods for the nonlocal Fowler equation"],"prefix":"10.1090","volume":"83","author":[{"given":"Afaf","family":"Bouharguane","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00e9mi","family":"Carles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2013,8,5]]},"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02757-3\/S0025-5718-2013-02757-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02757-3\/S0025-5718-2013-02757-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:53:30Z","timestamp":1776794010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2014-83-287\/S0025-5718-2013-02757-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,5]]},"references-count":0,"journal-issue":{"issue":"287","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["S0025-5718-2013-02757-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2013-02757-3","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2013,8,5]]}}}