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By extending the ideas of our recent work on global Richardson extrapolation, we now utilize some advanced versions of RE in the form of repeated RE (RRE). Assume that the underlying LMM\u2014the base method\u2014has order\n                    <jats:italic>p<\/jats:italic>\n                    and RE is applied\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u2113<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    times. Then, we prove that the accelerated sequence has convergence order\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$p+\\ell $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mi>\u2113<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . The version we present here is global RE (GRE, also known as passive RE), since the terms of the linear combinations are calculated independently. Thus, the resulting higher-order LMM-RGRE methods can be implemented in a parallel fashion and existing LMM codes can directly be used without any modification. We also investigate how the linear stability properties of the base method (e.g.,\n                    <jats:italic>A<\/jats:italic>\n                    - or\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$A(\\alpha )$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mi>\u03b1<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -stability) are preserved by the LMM-RGRE methods.\n                  <\/jats:p>","DOI":"10.1007\/s10998-025-00654-0","type":"journal-article","created":{"date-parts":[[2025,5,25]],"date-time":"2025-05-25T03:43:22Z","timestamp":1748144602000},"page":"329-340","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Linear multistep methods with repeated global Richardson extrapolation"],"prefix":"10.1007","volume":"91","author":[{"given":"I.","family":"Fekete","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"L\u00f3czi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,25]]},"reference":[{"key":"654_CR1","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1007\/978-3-030-55347-0_22","volume":"902","author":"T Bayleyegn","year":"2020","unstructured":"T. Bayleyegn, \u00c1. Havasi, Multiple Richardson Extrapolation Applied to Explicit Runge-Kutta Methods. Advances in High Performance Computing. Springer 902, 262\u2013270 (2020). https:\/\/doi.org\/10.1007\/978-3-030-55347-0_22","journal-title":"Advances in High Performance Computing. Springer"},{"key":"654_CR2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400833344","author":"DS Bernstein","year":"2009","unstructured":"D.S. Bernstein, Matrix Mathematics. Princeton Univ. Press (2009). https:\/\/doi.org\/10.1515\/9781400833344","journal-title":"Princeton Univ. Press"},{"key":"654_CR3","doi-asserted-by":"publisher","unstructured":"J.\u00a0C.\u00a0Butcher, Numerical Methods for Ordinary Differential Equations, 3rd edition, Wiley (2016), https:\/\/doi.org\/10.1002\/9781119121534","DOI":"10.1002\/9781119121534"},{"key":"654_CR4","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01601932","volume":"30","author":"P Deuflhard","year":"1979","unstructured":"P. Deuflhard, A Study of Extrapolation Methods Based on Multistep Schemes without Parasitic Solutions. J. Appl. Math. Phys. (ZAMP) 30, 177\u2013189 (1979). https:\/\/doi.org\/10.1007\/BF01601932","journal-title":"J. Appl. Math. Phys. (ZAMP)"},{"issue":"4","key":"654_CR5","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1137\/1027140","volume":"27","author":"P Deuflhard","year":"1985","unstructured":"P. Deuflhard, Recent Progress in Extrapolation Methods for Ordinary Differential Equations. SIAM Review 27(4), 505\u2013535 (1985). https:\/\/doi.org\/10.1137\/1027140","journal-title":"SIAM Review"},{"key":"654_CR6","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1553\/etna_vol54s210","volume":"54","author":"RD Falgout","year":"2021","unstructured":"R.D. Falgout, T.A. Manteuffel, B. O\u2019Neill, J.B. Schroder, Multigrid reduction in time with Richardson extrapolation. Electron. Trans. Numer. 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