{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:39:32Z","timestamp":1776832772826,"version":"3.51.2"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"324","license":[{"start":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003768","name":"Universit\u00c3\u00a9 de Strasbourg","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003768","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The equivalence between semi-Lagrangian and Lagrange\u2013Galerkin schemes has been proved by R. Ferretti [J. Comp. Math. 28 (2010), no. 4, 461\u2013473], [Numerische Mathematik 124 (2012), no. 1, 31\u201356] for the case of centered Lagrange interpolation of odd degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p less-than-or-equal-to 13\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>13<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p\\le 13<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We generalize this result to an\n                    <italic>arbitrary<\/italic>\n                    odd degree, for both the case of constant- and variable-coefficient equations. In addition, we prove that the same holds for spline interpolations.\n                  <\/p>","DOI":"10.1090\/mcom\/3494","type":"journal-article","created":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T09:16:57Z","timestamp":1573031817000},"page":"1783-1805","source":"Crossref","is-referenced-by-count":6,"title":["Stability of semi-Lagrangian schemes of arbitrary odd degree under constant and variable advection speed"],"prefix":"10.1090","volume":"89","author":[{"given":"Roberto","family":"Ferretti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Mehrenberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"A. Aldroubi, M. Unser, and M. Eden, Cardinal spline filters: Stability and convergence to the ideal sinc interpolator, Signal Processing 28 (1992), no. 2, 127\u2013138.","DOI":"10.1016\/0165-1684(92)90030-Z"},{"issue":"261","key":"2","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1090\/S0025-5718-07-01912-6","article-title":"Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system","volume":"77","author":"Besse, Nicolas","year":"2008","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","unstructured":"F. Boyer, Lecture notes (in french): Aspects th\u00e9oriques et num\u00e9riques de l\u2019\u00e9quation de transport, Aix-Marseille University, June 2014, \\url{https:\/\/www.math.univ-toulouse.fr\/~fboyer\/_media\/enseignements\/cours_transport_fboyer.pdf}."},{"key":"4","series-title":"Applied Mathematical Sciences","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6333-3","volume-title":"A practical guide to splines","volume":"27","author":"de Boor, Carl","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0387903569"},{"key":"5","unstructured":"L. Demanet, Lecture notes for course 18.330 \u2013 Introduction to Numerical Analysis, MIT Open Courseware, http:\/\/ocw.mit.edu."},{"key":"6","unstructured":"NIST Digital Library of Mathematical Functions, http:\/\/dlmf.nist.gov\/, Release 1.0.18 of 2018-03-27, F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller and B. V. 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Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0254-9409","issn-type":"print"},{"key":"10","doi-asserted-by":"crossref","unstructured":"R. Ferretti, On the relationship between Semi-Lagrangian and Lagrange\u2013Galerkin schemes, Numerische Mathematik 124 (2012), no. 1, 31\u201356.","DOI":"10.1007\/s00211-012-0505-5"},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s10915-013-9701-4","article-title":"Stability of some generalized Godunov schemes with linear high-order reconstructions","volume":"57","author":"Ferretti, Roberto","year":"2013","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"issue":"3","key":"12","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1007\/s10915-017-0509-5","article-title":"Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations","volume":"74","author":"Latu, Guillaume","year":"2018","journal-title":"J. Sci. 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