{"title":"New efficient four-stage implicit trigonometrically fitted modified RKN for second-order ODEs","authors":"Bingzhen Chen , Yuna Zhao , Wenjuan Zhai","doi":"10.1016/j.jocs.2024.102370","DOIUrl":null,"url":null,"abstract":"<div><p>The construction of implicit RKN is investigated in this paper. We finally obtain four four-stages implicit integrators by considering the symmetric, symplectic, and trigonometric fitting conditions. For the new obtained methods, we analyze their global convergence and stability property. And we carry out numerical experiments on some commonly considered problems in the literature. In view of the numerical experiments, we observe that the new methods outperform several efficient RKN methods in terms of accuracy and efficiency.</p></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1877750324001637","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
The construction of implicit RKN is investigated in this paper. We finally obtain four four-stages implicit integrators by considering the symmetric, symplectic, and trigonometric fitting conditions. For the new obtained methods, we analyze their global convergence and stability property. And we carry out numerical experiments on some commonly considered problems in the literature. In view of the numerical experiments, we observe that the new methods outperform several efficient RKN methods in terms of accuracy and efficiency.
期刊介绍：
Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory.
The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation.
This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods.
Computational science typically unifies three distinct elements:
• Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous);
• Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems;
• Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).
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