INVERSE PROBLEM SOLUTION FOR THE HEAT EQUATION

Authors

  • Rashidova Munisaxon Alisher qizi Master’s Student, National University of Uzbekistan named after Mirzo Ulugbek

Keywords:

Heat equation, inverse problem, Fourier method, Volterra integral equation, numerical solution, Python, heat flux, mathematical modeling.

Abstract

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.

References

Fayazov K.S., Khajiyev I.O. Incorrect and Inverse Problems. Textbook. – T.: "Ma'rifat", 2024. 176 p.

Zikirov O.S. Equations of Mathematical Physics (textbook). – T.: "Fan va texnologiya", 2017. 320 p.

Denisov A.M. Introduction to the Theory of Inverse Problems. Textbook. – M.: Moscow State University Press, 1994. – 207 p.

Isroilov M. Computational Methods: Textbook for Higher Education Institutions. Part 2. – Tashkent: "Iqtisodiyot-Moliya", 2008. – 320 p.

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Published

2026-04-04

How to Cite

Rashidova Munisaxon Alisher qizi. (2026). INVERSE PROBLEM SOLUTION FOR THE HEAT EQUATION. Ethiopian International Journal of Multidisciplinary Research, 13(4), 293–298. Retrieved from https://eijmr.org/index.php/eijmr/article/view/5924

Issue

Vol. 13 No. 4 (2026): Ethiopian International Journal of Multidisciplinary Research

Section

Articles