{"title":"十四阶相拟合方法的应用，以提高化学问题的解决","authors":"Chia-Liang Lin, T. E. Simos","doi":"10.1007/s10910-024-01701-w","DOIUrl":null,"url":null,"abstract":"<div><p>By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The <b>cost-efficient approach</b> is a new strategy whose aims are to boost algebraic order (<i>AOR</i>) and reduce function evaluations (<i>FEVs</i>). The symbolic representation of the one-of-a-kind approach is <i>PF</i>6<i>DPHFITN</i>142<i>SPS</i>. This method is infinitely periodic since it is <b>P-Stable</b>. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires <span>\\(5 \\, FEVs\\)</span>, the new method could be seen as a cost-effective strategy. With a <i>AOR</i> of 14, we can greatly enhance our current situation.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 4","pages":"919 - 961"},"PeriodicalIF":1.7000,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The application of a fourteenth-order phase-fitting approach to enhance chemical problem-solving\",\"authors\":\"Chia-Liang Lin, T. E. Simos\",\"doi\":\"10.1007/s10910-024-01701-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The <b>cost-efficient approach</b> is a new strategy whose aims are to boost algebraic order (<i>AOR</i>) and reduce function evaluations (<i>FEVs</i>). The symbolic representation of the one-of-a-kind approach is <i>PF</i>6<i>DPHFITN</i>142<i>SPS</i>. This method is infinitely periodic since it is <b>P-Stable</b>. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires <span>\\\\(5 \\\\, FEVs\\\\)</span>, the new method could be seen as a cost-effective strategy. With a <i>AOR</i> of 14, we can greatly enhance our current situation.</p></div>\",\"PeriodicalId\":648,\"journal\":{\"name\":\"Journal of Mathematical Chemistry\",\"volume\":\"63 4\",\"pages\":\"919 - 961\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-01-31\",\"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/s10910-024-01701-w\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-024-01701-w","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
The application of a fourteenth-order phase-fitting approach to enhance chemical problem-solving
By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The cost-efficient approach is a new strategy whose aims are to boost algebraic order (AOR) and reduce function evaluations (FEVs). The symbolic representation of the one-of-a-kind approach is PF6DPHFITN142SPS. This method is infinitely periodic since it is P-Stable. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires \(5 \, FEVs\), the new method could be seen as a cost-effective strategy. With a AOR of 14, we can greatly enhance our current situation.
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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