Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
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算法 924：TIDES，微分方程的泰勒级数积分器
DOI：
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发表时间：
2012
期刊：
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通讯作者：
Marcos Rodríguez
中科院分区：
文献类型：
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作者：
A. Abad;R. Barrio;F. Blesa;Marcos Rodríguez
本文介绍了TIDES软件包，并回顾了泰勒级数法在常微分方程数值积分中的应用。TIDES软件包为标准的双精度积分提供了一个易于使用的接口，也可用于四精度和多精度积分。开发该软件包的动机是越来越多的科学学科需要非常高精度的常微分方程解，而标准的常微分方程方法无法达到这些精度水平。TIDES软件包结合了Mathematica中的预处理器步骤，该步骤生成Fortran或C程序以及C中的库。TIDES的另一个功能是直接求解ODE系统解的灵敏度，这意味着我们可以计算任何阶变分方程的解，而无需显式地制定它们。讨论了软件的不同选项，最后将其与其他已知的可用方法以及TIDES的不同选项进行了比较。从数值测试来看，TIDES在速度和精度方面都具有标准方法的竞争力，但它也提供了新的功能。
This article introduces the software package TIDES and revisits the use of the Taylor series method for the numerical integration of ODEs. The package TIDES provides an easy-to-use interface for standard double precision integrations, but also for quadruple precision and multiple precision integrations. The motivation for the development of this package is that more and more scientific disciplines need very high precision solution of ODEs, and a standard ODE method is not able to reach these precision levels. The TIDES package combines a preprocessor step in Mathematica that generates Fortran or C programs with a library in C. Another capability of TIDES is the direct solution of sensitivities of the solution of ODE systems, which means that we can compute the solution of variational equations up to any order without formulating them explicitly. Different options of the software are discussed, and finally it is compared with other well-known available methods, as well as with different options of TIDES. From the numerical tests, TIDES is competitive, both in speed and accuracy, with standard methods, but it also provides new capabilities.