{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T07:17:53Z","timestamp":1777274273959,"version":"3.51.4"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"292","license":[{"start":{"date-parts":[[2015,7,17]],"date-time":"2015-07-17T00:00:00Z","timestamp":1437091200000},"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>\n                    We present one nonlinear and one linearized numerical schemes for the nonlinear epitaxial growth model without slope selection. Both schemes are proved to be uniquely solvable and convergent with the convergence rate of order two in a discrete\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">L_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm. By introducing an auxiliary variable in the discrete energy functional, the energy stability of both schemes is guaranteed regardless of the time step size, in the sense that a modified energy is monotonically nonincreasing in discrete time. Numerical experiments are carried out to support the theoretical claims.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2014-02874-3","type":"journal-article","created":{"date-parts":[[2014,7,17]],"date-time":"2014-07-17T10:06:05Z","timestamp":1405591565000},"page":"653-674","source":"Crossref","is-referenced-by-count":42,"title":["Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection"],"prefix":"10.1090","volume":"84","author":[{"given":"Zhonghua","family":"Qiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-zhong","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengru","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,7,17]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1093\/imanum\/13.1.115","article-title":"Finite difference discretization of the cubic Schr\u00f6dinger equation","volume":"13","author":"Akrivis, Georgios D.","year":"1993","journal-title":"IMA J. 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