{"title":"Precise Numerical Differentiation of Thermodynamic Functions with\n Multicomplex Variables","authors":"U. Deiters, I. Bell","doi":"10.6028/jres.126.033","DOIUrl":null,"url":null,"abstract":"The multicomplex finite-step method for numerical differentiation is an extension\n of the popular Squire–Trapp method, which uses complex arithmetics to compute\n first-order derivatives with almost machine precision. In contrast to this, the\n multicomplex method can be applied to higher-order derivatives. Furthermore, it can be\n applied to functions of more than one variable and obtain mixed derivatives. It is\n possible to compute various derivatives at the same time. This work demonstrates the\n numerical differentiation with multicomplex variables for some thermodynamic problems.\n The method can be easily implemented into existing computer programs, applied to\n equations of state of arbitrary complexity, and achieves almost machine precision for\n the derivatives. Alternative methods based on complex integration are discussed,\n too.","PeriodicalId":54766,"journal":{"name":"Journal of Research of the National Institute of Standards and Technology","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Institute of Standards and Technology","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.6028/jres.126.033","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 2
Abstract
The multicomplex finite-step method for numerical differentiation is an extension
of the popular Squire–Trapp method, which uses complex arithmetics to compute
first-order derivatives with almost machine precision. In contrast to this, the
multicomplex method can be applied to higher-order derivatives. Furthermore, it can be
applied to functions of more than one variable and obtain mixed derivatives. It is
possible to compute various derivatives at the same time. This work demonstrates the
numerical differentiation with multicomplex variables for some thermodynamic problems.
The method can be easily implemented into existing computer programs, applied to
equations of state of arbitrary complexity, and achieves almost machine precision for
the derivatives. Alternative methods based on complex integration are discussed,
too.
期刊介绍：
The Journal of Research of the National Institute of Standards and Technology is the flagship publication of the National Institute of Standards and Technology. It has been published under various titles and forms since 1904, with its roots as Scientific Papers issued as the Bulletin of the Bureau of Standards.
In 1928, the Scientific Papers were combined with Technologic Papers, which reported results of investigations of material and methods of testing. This new publication was titled the Bureau of Standards Journal of Research.
The Journal of Research of NIST reports NIST research and development in metrology and related fields of physical science, engineering, applied mathematics, statistics, biotechnology, information technology.
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