{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T09:09:08Z","timestamp":1774688948815,"version":"3.50.1"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"333","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["850941"],"award-info":[{"award-number":["850941"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We study a filtered Lie splitting scheme for the cubic nonlinear Schr\u00f6dinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript s\">\n  <mml:semantics>\n    <mml:msup>\n      <mml:mi>H<\/mml:mi>\n      <mml:mi>s<\/mml:mi>\n    <\/mml:msup>\n    <mml:annotation encoding=\"application\/x-tex\">H^s<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> with <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"0 greater-than s greater-than 1\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mn>0<\/mml:mn>\n      <mml:mo>&gt;<\/mml:mo>\n      <mml:mi>s<\/mml:mi>\n      <mml:mo>&gt;<\/mml:mo>\n      <mml:mn>1<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">0&gt;s&gt;1<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> overcoming the standard stability restriction to smooth Sobolev spaces with index <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s greater-than 1 slash 2\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>s<\/mml:mi>\n      <mml:mo>&gt;<\/mml:mo>\n      <mml:mn>1<\/mml:mn>\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\n        <mml:mo>\/<\/mml:mo>\n      <\/mml:mrow>\n      <mml:mn>2<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">s&gt;1\/2<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> . More precisely, we prove convergence rates of order <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"tau Superscript s slash 2\">\n  <mml:semantics>\n    <mml:msup>\n      <mml:mi>\u03c4<\/mml:mi>\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\n        <mml:mi>s<\/mml:mi>\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\n          <mml:mo>\/<\/mml:mo>\n        <\/mml:mrow>\n        <mml:mn>2<\/mml:mn>\n      <\/mml:mrow>\n    <\/mml:msup>\n    <mml:annotation encoding=\"application\/x-tex\">\\tau ^{s\/2}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n  <mml:semantics>\n    <mml:msup>\n      <mml:mi>L<\/mml:mi>\n      <mml:mn>2<\/mml:mn>\n    <\/mml:msup>\n    <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> at this level of regularity.<\/p>","DOI":"10.1090\/mcom\/3676","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T13:30:30Z","timestamp":1624455030000},"page":"169-182","source":"Crossref","is-referenced-by-count":18,"title":["Error estimates at low regularity of splitting schemes for NLS"],"prefix":"10.1090","volume":"91","author":[{"given":"Alexander","family":"Ostermann","sequence":"first","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Rousset","sequence":"additional","affiliation":[]},{"given":"Katharina","family":"Schratz","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,8,5]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1137\/S1064827501393253","article-title":"Numerical study of time-splitting spectral discretizations of nonlinear Schr\u00f6dinger equations in the semiclassical regimes","volume":"25","author":"Bao, Weizhu","year":"2003","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF01895688","article-title":"Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation","volume":"3","author":"Bourgain, J.","year":"1993","journal-title":"Geom. Funct. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1016-443X","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1016\/j.jmaa.2016.05.014","article-title":"Fractional error estimates of splitting schemes for the nonlinear Schr\u00f6dinger equation","volume":"442","author":"Eilinghoff, Johannes","year":"2016","journal-title":"J. Math. Anal. 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