{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:40:53Z","timestamp":1760146853972,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,14]],"date-time":"2024-12-14T00:00:00Z","timestamp":1734134400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Free University of Bozen-Bolzano (IN200Z SmartPrint)","award":["I53C22002100003"],"award-info":[{"award-number":["I53C22002100003"]}]},{"name":"Provincia Autonoma di Bolzano\/Alto Adige\u2014Ripartizione Innovazione, Ricerca, Universit\u00e0 e Musei","award":["I53C22002100003"],"award-info":[{"award-number":["I53C22002100003"]}]},{"name":"INdAM-GNCS","award":["I53C22002100003"],"award-info":[{"award-number":["I53C22002100003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this study, we develop new efficient parallel techniques for solving both distinct and multiple roots of nonlinear problems at the same time. The parallel techniques represent an innovative contribution to the discipline, with local convergence of the ninth order. Theoretical research shows the rapid convergence and effectiveness of the proposed parallel schemes. To assess the suggested scheme\u2019s stability and consistency, we look at certain biomedical engineering applications, such as osteoporosis in Chinese women, blood rheology, and differential equations. Overall, detailed analyses of convergence behavior, memory utilization, computational time, and percentage computational efficiency show that the novel parallel techniques outperform the traditional methods. The proposed methods would be more suitable for large-scale computational problems in biomedical applications due to their advantages in memory efficiency, CPU time, and error reduction.<\/jats:p>","DOI":"10.3390\/a17120575","type":"journal-article","created":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T10:08:53Z","timestamp":1734343733000},"page":"575","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational Analysis of Parallel Techniques for Nonlinear Biomedical Engineering Problems"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2980-5801","authenticated-orcid":false,"given":"Mudassir","family":"Shams","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, Italy"},{"name":"Department of Mathematics, Bal\u0131kesir University, 10145 Bal\u0131kesir, Turkey"},{"name":"Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"Carpentieri","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Free University of Bozen-Bolzano (BZ), 39100 Bolzano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cropley, D.H. 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