{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T15:43:50Z","timestamp":1763480630902,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T00:00:00Z","timestamp":1670371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["22-19-00573"],"award-info":[{"award-number":["22-19-00573"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients. However, multistep composition schemes are much less-known and investigated in the literature due to their complex nature. In this paper, we propose several novel schemes for solving ordinary differential equations based on the composition of adjoint multistep methods. Numerical stability, energy preservation, and performance of proposed schemes are investigated theoretically and experimentally using a set of differential problems. The applicability and efficiency of the proposed composition multistep methods are discussed.<\/jats:p>","DOI":"10.3390\/a15120463","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T03:27:57Z","timestamp":1670383677000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Numerical Integration Schemes Based on Composition of Adjoint Multistep Methods"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5119-2274","authenticated-orcid":false,"given":"Dmitriy","family":"Pesterev","sequence":"first","affiliation":[{"name":"Computer-Aided Design Department, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0672-3475","authenticated-orcid":false,"given":"Olga","family":"Druzhina","sequence":"additional","affiliation":[{"name":"Youth Research Institute, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4136-1227","authenticated-orcid":false,"given":"Alexander","family":"Pchelintsev","sequence":"additional","affiliation":[{"name":"Department of Higher Mathematics, Tambov State Technical University, 106 Sovetskaya St., 392000 Tambov, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5841-2193","authenticated-orcid":false,"given":"Erivelton","family":"Nepomuceno","sequence":"additional","affiliation":[{"name":"Centre for Ocean Energy Research, Department of Electronic Engineering, Maynooth University, W23 X021 Maynooth, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8941-4220","authenticated-orcid":false,"given":"Denis","family":"Butusov","sequence":"additional","affiliation":[{"name":"Youth Research Institute, St. Petersburg Electrotechnical University \u201cLETI\u201d, 5 Professora Popova St., 197376 Saint Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,7]]},"reference":[{"key":"ref_1","unstructured":"Hairer, E., Lubich, C., and Wanner, G. 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