{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,21]],"date-time":"2026-06-21T06:31:36Z","timestamp":1782023496972,"version":"3.54.5"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"name":"Guanghua Talent Project of SWUFE"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071216"],"award-info":[{"award-number":["12071216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101510"],"award-info":[{"award-number":["12101510"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation of Sichuan Province","award":["2022NSFSC1789"],"award-info":[{"award-number":["2022NSFSC1789"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2023,10,31]]},"DOI":"10.1137\/22m1520050","type":"journal-article","created":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T18:36:46Z","timestamp":1696271806000},"page":"2157-2181","source":"Crossref","is-referenced-by-count":37,"title":["Discrete Gradient Structure of a Second-Order Variable-Step Method for Nonlinear Integro-Differential Models"],"prefix":"10.1137","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0777-6832","authenticated-orcid":true,"given":"Hong-lin","family":"Liao","sequence":"first","affiliation":[{"name":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China; Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6947-6838","authenticated-orcid":true,"given":"Pin","family":"Lyu","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,9,28]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0033-569X-2015-01386-2"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2003.09.001"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543234"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-06-01788-1"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902402481"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2010.04.016"},{"key":"ref7","volume-title":"Relativistic Quantum Mechanics: Wave Equation","author":"Greiner W.","year":"1994"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/19M1259675"},{"key":"ref9","author":"Ji B.","journal-title":"Commun. Math. Sci."},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2016-0136"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/0732083"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/16M1175742"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2020-0124"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/20M1384105"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109473"},{"key":"ref16","author":"Liao H.-L.","year":"2023","journal-title":"Sci. China Math."},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3585"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.4208\/nmtma.OA-2022-0011s"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00677-1"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-022-02000-9"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1142\/p614"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0045-y"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00025-9"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1017\/S0334270000007268"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2000-00364-5"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drn075"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/19M1260475"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/120880719"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drt048"},{"key":"ref30","first-page":"739","volume":"123","author":"Nigmatullin R. R.","year":"1984","journal-title":"Phys. B"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.4208\/csiam-am.2020-0024"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082329"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/18M1203560"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T15:48:22Z","timestamp":1704988102000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1520050"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,28]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10,31]]}},"alternative-id":["10.1137\/22M1520050"],"URL":"https:\/\/doi.org\/10.1137\/22m1520050","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,28]]}}}