Abstract This paper is dedicated to numerical computation of higher order derivatives in Simulink. In this paper, a new module has been implemented to achieve this purpose within the Simulink-based Infinity Computer solution, recently introduced by the authors. This module offers several blocks to calculate higher order derivatives of a function given by the arithmetic operations and elementary functions. Traditionally, this can be done in Simulink using finite differences only, for which it is well-known that they can be characterized by instability and low accuracy. Moreover, the proposed module allows to calculate higher order Lie derivatives embedded in the numerical solution to Ordinary Differential Equations (ODEs). Traditionally, Simulink does not offer any practical solution for this case without using difficult external libraries and methodologies, which are domain-specific, not general-purpose and have their own limitations. The proposed differentiation module bridges this gap, is simple and does not require any additional knowledge or skills except basic knowledge of the Simulink programming language. Finally, the block for constructing the Taylor expansion of the differentiated function is also proposed, adding so another efficient numerical method for solving ODEs and for polynomial approximation of the functions. Numerical experiments on several classes of test problems confirm advantages of the proposed solution.

中文翻译：

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基于 Simulink 的软件解决方案，使用 Infinity Computer 方法进行高阶微分

摘要 本文致力于在Simulink 中进行高阶导数的数值计算。在本文中，作者最近在基于 Simulink 的 Infinity Computer 解决方案中实施了一个新模块来实现此目的。该模块提供了几个模块来计算由算术运算和初等函数给出的函数的高阶导数。传统上，这只能在 Simulink 中使用有限差分来完成，众所周知，它们的特点是不稳定性和低精度。此外，所提出的模块允许计算嵌入在常微分方程 (ODE) 数值解中的高阶 Lie 导数。传统上，如果不使用困难的外部库和方法，Simulink 不会为这种情况提供任何实用的解决方案，这些库和方法是特定于领域的，不是通用的，并且有其自身的局限性。提议的微分模块弥补了这一差距，简单且除了 Simulink 编程语言的基本知识外，不需要任何其他知识或技能。最后，还提出了用于构造微分函数的泰勒展开式的块，从而增加了另一种求解 ODE 和函数多项式逼近的有效数值方法。对几类测试问题的数值实验证实了所提出的解决方案的优点。很简单，除了 Simulink 编程语言的基本知识外，不需要任何额外的知识或技能。最后，还提出了用于构造微分函数的泰勒展开式的块，从而增加了另一种求解 ODE 和函数多项式逼近的有效数值方法。对几类测试问题的数值实验证实了所提出的解决方案的优点。很简单，除了 Simulink 编程语言的基本知识外，不需要任何额外的知识或技能。最后，还提出了用于构造微分函数的泰勒展开式的块，从而增加了另一种求解 ODE 和函数多项式逼近的有效数值方法。对几类测试问题的数值实验证实了所提出的解决方案的优点。