{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T07:04:49Z","timestamp":1761980689627,"version":"build-2065373602"},"reference-count":14,"publisher":"SAGE Publications","issue":"11","license":[{"start":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T00:00:00Z","timestamp":1753833600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>The growing intricacy of contemporary engineering systems, typically reduced to differential equations, poses a difficulty in digitally simulating them. The linearly implicit quantized state system (LIQSS) provides a different method from traditional numerical integration techniques for tackling such problems. This method is effective in large sparse stiff systems and systems with frequent discontinuities. However, this method could be further improved. First, the algorithm can step through the solution analytically or through iterations. A comparison is presented in this article. Second, the intrinsic discrete behavior of this new method can cause oscillations that lead to small unnecessary simulation steps. A prior approach was made to detect and terminate these cycles. Different detection mechanisms are examined in this article. Third, a linear approximation was used. Its enhancement is also investigated in this work. Finally, the article provides which of these modifications improved the overall performance of some systems simulations using LIQSS order one.<\/jats:p>","DOI":"10.1177\/00375497251351941","type":"journal-article","created":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:04:06Z","timestamp":1753869846000},"page":"1153-1164","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Improving the modified linearly implicit quantized state system methods: step size, cycle detection, and linear approximation coefficient"],"prefix":"10.1177","volume":"101","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1230-5488","authenticated-orcid":false,"given":"Elmongi","family":"Elbellili","sequence":"first","affiliation":[{"name":"Royal Military Academy, Belgium"},{"name":"KU Leuven, Belgium"}]},{"given":"Philippe","family":"Blondeel","sequence":"additional","affiliation":[{"name":"Royal Military Academy, Belgium"}]},{"given":"Daan","family":"Huybrechs","sequence":"additional","affiliation":[{"name":"KU Leuven, Belgium"}]},{"given":"Ben","family":"Lauwens","sequence":"additional","affiliation":[{"name":"Royal Military Academy, Belgium"}]}],"member":"179","published-online":{"date-parts":[[2025,7,30]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09947-6"},{"key":"e_1_3_3_3_2","volume-title":"Solving ordinary differential equations I: nonstiff problems","author":"Hairer E","year":"1993","unstructured":"Hairer E, N\u00f8rsett S, Wanner G. Solving ordinary differential equations I: nonstiff problems. 2nd ed. Berlin: Springer, 1993.","edition":"2"},{"key":"e_1_3_3_4_2","volume-title":"Continuous system simulation","author":"Cellier F","year":"2006","unstructured":"Cellier F, Kofman E. Continuous system simulation. New York: Springer, 2006."},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.simpat.2013.03.004"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1177\/00375497241230985"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1177\/0037549718766689"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1177\/0037549711403645"},{"key":"e_1_3_3_9_2","first-page":"428","volume-title":"2022 annual modeling and simulation conference (ANNSIM)","author":"Mahawattege R","unstructured":"Mahawattege R, Nutaro J. Aquantized state integrator with second order errors over monotonic segments. In: 2022 annual modeling and simulation conference (ANNSIM), San Diego, CA, 18\u201320 July 2022, pp. 428\u2013436. San Diego, CA: Society for Modeling & Simulation International (SCS)."},{"key":"e_1_3_3_10_2","first-page":"231","article-title":"Relative error control in quantization based integration","volume":"39","author":"Kofman E.","year":"2009","unstructured":"Kofman E. Relative error control in quantization based integration. Lat Am Appl Res 2009; 39: 231\u2013238.","journal-title":"Lat Am Appl Res"},{"key":"e_1_3_3_11_2","first-page":"469","volume-title":"Proceedings of the 3rd international conference on computational modeling, simulation and optimization","author":"Elbellili E","unstructured":"Elbellili E, Lauwens B, Huybrechs D. Investigation of different conditions to detect cycles in linearly implicit quantized state systems. In: Proceedings of the 3rd international conference on computational modeling, simulation and optimization, Phuket, Thailand, 14\u201316 June 2024, pp. 469\u2013473. New York: IEEE."},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1177\/0037549714536255"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.5334\/jors.151"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.88.16.7328"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.1177\/0037549715616683"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/00375497251351941","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/00375497251351941","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/00375497251351941","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T07:00:29Z","timestamp":1761980429000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/00375497251351941"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,30]]},"references-count":14,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["10.1177\/00375497251351941"],"URL":"https:\/\/doi.org\/10.1177\/00375497251351941","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"type":"print","value":"0037-5497"},{"type":"electronic","value":"1741-3133"}],"subject":[],"published":{"date-parts":[[2025,7,30]]}}}