title: ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð¿Ð¾ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð² ÑÐ¾ÑÐºÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Algorithm for solving the inverse problem of determining the initial temperature distribution based on temperature measurements at a point
Creators: name: Ð¨Ð¸ÑÑÐµÐ², ÐÐ»ÐµÐ±
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2025
Subjects: Ð¾Ð±ÑÐ°ÑÐ½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ°
ÑÐµÐ¿Ð»Ð¾Ð¿ÐµÑÐµÐ´Ð°ÑÐ°
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ
python
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼
inverse problems
heat transfer
numerical modeling
initial temperature distribution
algorithm

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description: The purpose of this work is to develop and implement an algorithm for solving the inverse problem of determining the initial temperature distribution based on temperature measurements at one point, including the creation of a software tool for performing calculations and analyzing the results. Tasks that were solved during the study: Conducting a literature review on the topic of the study and studying existing methods for solving direct and inverse heat conductivity problems. Developing a mathematical model and algorithm for solving the inverse heat conductivity problem. Creating a software prototype for numerically solving the problem, visualizing the results and analyzing the data obtained. Testing the developed prototype and analyzing its effectiveness. The work included mathematical modeling using the finite difference method for numerically solving the problem. Algorithms for calculations on various time and spatial grids, as well as functions for visualizing temperature distributions, were implemented. As a result of the work: A program has been developed that provides a solution to direct and inverse heat conductivity problems with the ability to customize the parameters. Various tests of the program have been carried out. Recommendations for further development of the algorithm have been formed. The proposed method can be applied in various engineering problems related to thermal processes, as well as in research and educational activities for the analysis of heat transfer phenomena.