Formalization of Euler–Lagrange Equation Set Based on Variational Calculus in HOL Light

Guan, Yong; Zhang, Jingzhi; Wang, Guohui; Li, Ximeng; Shi, Zhiping

doi:10.1007/s10817-020-09549-w

Cited by 3 publications

(1 citation statement)

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“…However, both these approaches rely on approximating the solutions of differential equations representing the dynamical behavior of the underlying system. Guan et al [15] used the HOL Light theorem prover to formalize the Euler-Lagrange equation set that is based on Gâutex derivatives. In addition, the authors used their proposed formalization for formally verifying the least resistance problem of gas flow.…”

Section: Related Workmentioning

confidence: 99%

On the Formalization of the Heat Conduction Problem in HOL

Deniz¹,

Rashid²,

Hasan³

et al. 2022

Preprint

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Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the temperature distribution and diffusion of heat within a body. Due to the wider utility of these equations in various safety-critical applications, such as thermal protection systems, a formal analysis of the heat transfer is of utmost importance. In this paper, we propose to use higher-order-logic (HOL) theorem proving for formally analyzing the heat conduction problem in rectangular coordinates. In particular, we formally model the heat transfer as a one-dimensional heat equation for a rectangular slab using the multivariable calculus theories of the HOL Light theorem prover. This requires the formalization of the heat operator and formal verification of its various properties, such as linearity and scaling. Moreover, we use the separation of variables method for formally verifying the solution of the PDEs, which allows modeling the heat transfer in the slab under various initial and boundary conditions using HOL Light.

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Section: Related Workmentioning

confidence: 99%