Finding the Projection of a Third-Kind Ill-Posed Boundary Value Problem in the Heat Scattering Equation

Rustamov Maxammadali  Jabborovich; Ubaydullayev Noyob Nodir  o’g’li

Rustamov Maxammadali Jabborovich Associate professor, candidate of physical and mathematical sciences Jizzakh branch of the National University of Uzbekistan named after Mirzo Ulugbek
Ubaydullayev Noyob Nodir o’g’li Master of the Jizzakh branch of the National University of Uzbekistan named after Mirzo Ulugbek

Keywords: ill-posed boundary value problems, projection method, heat scattering equation, Tikhonov regularization, numerical simulations

Abstract

This article proposes a projection method for finding the projection of a third-kind ill-posed boundary value problem in the heat scattering equation. Previous approaches have limitations in terms of accuracy and efficiency, and the proposed method overcomes these limitations by using a projection operator to obtain a well-posed problem. Numerical simulations demonstrate the effectiveness of the method, which has potential applications in various fields, such as heat transfer and material science. Further research can explore the applicability of the method to more complex problems and the extension of the method to other types of ill-posed problems.

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