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

Main Article Content

Rustamov Maxammadali Jabborovich
Ubaydullayev Noyob Nodir o’g’li


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.

Article Details

How to Cite
Jabborovich, R. M., & o’g’li, U. N. N. (2023). Finding the Projection of a Third-Kind Ill-Posed Boundary Value Problem in the Heat Scattering Equation. International Journal on Orange Technologies, 5(5), 40-47. Retrieved from


1. Ivanov, V. K., & Kalantarov, V. K. (1994). Inverse problems for partial differential equations (Vol. 146). Springer Science & Business Media.
2. Hansen, P. C. (2010). Discrete inverse problems: insight and algorithms (Vol. 7). SIAM.
3. Engl, H. W., Hanke, M., & Neubauer, A. (1996). Regularization of inverse problems (Vol. 375). Springer Science & Business Media.
4. Tikhonov, A. N., & Arsenin, V. Y. (1977). Solutions of ill-posed problems. John Wiley & Sons.
5. Kirsch, A. (2011). An introduction to the mathematical theory of inverse problems (Vol. 120). Springer Science & Business Media.
6. Hohage, T., & Werner, F. (2007). Tikhonov regularization for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximations. Inverse Problems, 23(5), 2279.
7. Hohage, T., & Raus, T. (2012). On the method of approximate Tikhonov regularization for linear ill-posed problems. Numerische Mathematik, 122(1), 71-98.
8. Pereverzev, S. V., & Schock, E. (2002). Regularization theory for ill-posed problems: selected topics. Inverse Problems, 18(6), R99.
9. Cheney, M., & Kincaid, D. (2009). Numerical mathematics and computing (Vol. 6). Cengage Learning.
10. Liu, Y., Huang, J., & Shen, L. (2019). A modified Tikhonov regularization method for ill-posed boundary value problems. Journal of Computational Physics, 386, 245-257.