{"title":"Precise Numerical Differentiation of Thermodynamic Functions with\u0000 Multicomplex Variables","authors":"U. Deiters, I. Bell","doi":"10.6028/jres.126.033","DOIUrl":"https://doi.org/10.6028/jres.126.033","url":null,"abstract":"The multicomplex finite-step method for numerical differentiation is an extension\u0000 of the popular Squire–Trapp method, which uses complex arithmetics to compute\u0000 first-order derivatives with almost machine precision. In contrast to this, the\u0000 multicomplex method can be applied to higher-order derivatives. Furthermore, it can be\u0000 applied to functions of more than one variable and obtain mixed derivatives. It is\u0000 possible to compute various derivatives at the same time. This work demonstrates the\u0000 numerical differentiation with multicomplex variables for some thermodynamic problems.\u0000 The method can be easily implemented into existing computer programs, applied to\u0000 equations of state of arbitrary complexity, and achieves almost machine precision for\u0000 the derivatives. Alternative methods based on complex integration are discussed,\u0000 too.","PeriodicalId":54766,"journal":{"name":"Journal of Research of the National Institute of Standards and Technology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48880861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}