{"title":"Adaptive second derivative multistep methods for solving stiff chemical problems","authors":"Mozhgan Eghbaljoo, Gholamreza Hojjati, Ali Abdi","doi":"10.1007/s10910-024-01582-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we introduce one-parameter families of multistep numerical methods for solving stiff initial value problems of ordinary differential equations. These methods are adaptive versions of second derivative backward differentiation formulas and their extensions. The stability properties of the proposed schemes are better than those of the main methods which make them suitable for solving stiff problems. Numerical experiments on some problems arising from chemical reactions verify the theoretical results.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-024-01582-z","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
In this paper, we introduce one-parameter families of multistep numerical methods for solving stiff initial value problems of ordinary differential equations. These methods are adaptive versions of second derivative backward differentiation formulas and their extensions. The stability properties of the proposed schemes are better than those of the main methods which make them suitable for solving stiff problems. Numerical experiments on some problems arising from chemical reactions verify the theoretical results.
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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