INVERSE PROBLEM SOLUTION FOR THE HEAT EQUATION

This article examines the inverse problem for the heat conduction equation. The primary objective of the research is to develop a method for reconstructing an unknown boundary function based on additional temperature data from an internal point of the object. The Fourier method of separation of variables was applied to solve the problem, which subsequently reduced it to a Volterra integral equation of the second kind. The proposed solution algorithm was numerically implemented in the Python programming language using the trapezoidal rule, and the obtained results were analyzed.本文针对热传导方程的反问题开展研究。本研究的核心目标是提出一种方法，可基于物体内部测点的附加温度数据，重构未知的边界函数。研究采用分离变量傅里叶法对该问题进行求解，将其转化为第二类沃尔泰拉（Volterra）积分方程。本研究通过Python编程语言结合梯形法则，对所提出的求解算法进行了数值实现，并对所得结果进行了分析。