{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:01:20Z","timestamp":1776834080223,"version":"3.51.2"},"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>\n                    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\n                    <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>\n                    with\n                    <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>\n                    overcoming the standard stability restriction to smooth Sobolev spaces with index\n                    <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>\n                    . More precisely, we prove convergence rates of order\n                    <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>\n                              \u03c4\n                              \n                            <\/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>\n                    in\n                    <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>\n                    at this level of regularity.\n                  <\/p>","DOI":"10.1090\/mcom\/3676","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T09:30:30Z","timestamp":1624440630000},"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":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Rousset","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katharina","family":"Schratz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"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. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-247X","issn-type":"print"},{"key":"4","series-title":"Zurich Lectures in Advanced Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.4171\/100","volume-title":"Geometric numerical integration and Schr\\\"{o}dinger equations","author":"Faou, Erwan","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9783037191002"},{"key":"5","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","volume-title":"Solving ordinary differential equations. I","volume":"8","author":"Hairer, E.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540566708","edition":"2"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"1366","DOI":"10.1137\/070683787","article-title":"Numerical dispersive schemes for the nonlinear Schr\u00f6dinger equation","volume":"47","author":"Ignat, Liviu I.","year":"2009","journal-title":"SIAM J. Numer. 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Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1615-3375","issn-type":"print"},{"key":"13","series-title":"CBMS Regional Conference Series in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/106","volume-title":"Nonlinear dispersive equations","volume":"106","author":"Tao, Terence","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/0821841432"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2022-91-333\/S0025-5718-2021-03676-5\/mcom3676_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/earlyview\/#mcom3676\/.pdf","content-type":"unspecified","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2022-91-333\/S0025-5718-2021-03676-5\/S0025-5718-2021-03676-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:19:48Z","timestamp":1776831588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2022-91-333\/S0025-5718-2021-03676-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,5]]},"references-count":13,"journal-issue":{"issue":"333","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["S0025-5718-2021-03676-5"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3676","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":[[2021,8,5]]}}}