Finding the Projection of a Third-Kind Ill-Posed Boundary Value Problem in the Heat Scattering Equation
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.
References
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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.
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.
Published
2023-05-12
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 https://journals.researchparks.org/index.php/IJOT/article/view/4365
Section
Articles
