多元复变热力学函数的精确数值微分

IF 1.3 4区工程技术 Q3 INSTRUMENTS & INSTRUMENTATION

Journal of Research of the National Institute of Standards and Technology Pub Date : 2021-11-29 DOI:10.6028/jres.126.033

U. Deiters, I. Bell

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引用次数: 2

摘要

数值微分的多重复数有限步法是流行的Squire–Trapp方法的扩展，该方法使用复数算法以几乎机器精度计算一阶导数。与此相反，多重复数方法可以应用于高阶导数。此外，它可以应用于一个以上变量的函数，并获得混合导数。可以同时计算各种导数。这项工作证明了一些热力学问题的多复变量数值微分。该方法可以很容易地实现到现有的计算机程序中，应用于任意复杂度的状态方程，并且可以实现导数的几乎机器精度。还讨论了基于复杂集成的替代方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Precise Numerical Differentiation of Thermodynamic Functions with Multicomplex Variables

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.

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来源期刊

Journal of Research of the National Institute of Standards and Technology 工程技术-物理：应用

自引率

33.30%

发文量

审稿时长

>12 weeks

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.