{"title":"A first-rate fourteenth-order phase-fitting approach to solving chemical problems","authors":"Mei Hong, Chia-Liang Lin, T. E. Simos","doi":"10.1007/s10910-024-01668-8","DOIUrl":null,"url":null,"abstract":"<p>Using a technique that accounts for disappearing phase-lag might lead to the elimination of phase-lag and all of its derivatives up to order four. The new technique known as the <b>cost-efficient approach</b> aims to improve algebraic order (<i>AOR</i>) and decrease function evaluations (<i>FEvs</i>). The one-of-a-kind approach is shown by Equation <i>PF</i>4<i>DPHFITN</i>142<i>SPS</i>. This method is endlessly periodic since it is <b>P-Stable</b>. The proposed method may be used to solve many different types of periodic and/or oscillatory problems. This innovative method was used to address the difficult issue of Schrödinger-type coupled differential equations in quantum chemistry. The new technique might be seen as a cost-efficient solution since it only requires 5<i>FEvs</i> to execute each step. We are able to greatly ameliorate our current situation with an AOR of 14.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-09-17","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://doi.org/10.1007/s10910-024-01668-8","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Using a technique that accounts for disappearing phase-lag might lead to the elimination of phase-lag and all of its derivatives up to order four. The new technique known as the cost-efficient approach aims to improve algebraic order (AOR) and decrease function evaluations (FEvs). The one-of-a-kind approach is shown by Equation PF4DPHFITN142SPS. This method is endlessly periodic since it is P-Stable. The proposed method may be used to solve many different types of periodic and/or oscillatory problems. This innovative method was used to address the difficult issue of Schrödinger-type coupled differential equations in quantum chemistry. The new technique might be seen as a cost-efficient solution since it only requires 5FEvs to execute each step. We are able to greatly ameliorate our current situation with an AOR of 14.
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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