SavedAdd your journal

Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2018 / Cilt: 8 - Sayı: 2

Reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation

Esra KARATAŞ AKGÜL
Pages
145–151
Publication Date
2022-10-11
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We prove the efficiency of the reproducingkernel Hilbert space method for solutions of a coefficient inverse problem forthe kinetic equation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:On the basis of a reproducing kernel Hilbert space, reproducing kernel functionsfor solving the coefficient inverse problem for the kinetic equation aregiven in this paper.
📊
Key Findings & Data:Reproducing kernel functions found in the reproducingkernel Hilbert space imply that they can be considered for solving such inverseproblems.
💡
Conclusion & Impact:We prove the efficiency of the reproducingkernel Hilbert space method for solutions of a coefficient inverse problem forthe kinetic equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

On the basis of a reproducing kernel Hilbert space, reproducing kernel functionsfor solving the coefficient inverse problem for the kinetic equation aregiven in this paper. Reproducing kernel functions found in the reproducingkernel Hilbert space imply that they can be considered for solving such inverseproblems. We obtain approximate solutions by reproducing kernel functions.We show our results by a table. We prove the efficiency of the reproducingkernel Hilbert space method for solutions of a coefficient inverse problem forthe kinetic equation.

🔖

Cite This Article

AKGÜL, E. K. (2022). Reproducing kernel Hilbert space method for solutions of a coefficient inverse problem for the kinetic equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 8 - Sayı: 2, 145–151. https://ajindex.com/articles/440652

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Golgeleyen, F., and Amirov, A. (2011). On the approximate solution of a coefficient inverse problem for the kinetic equation. Math. Commun. 16, 283-298.
  2. Perthame, B. (2014). Mathematical tools for kinetic equations, Bull. Amer. Math. Soc. 41, 205-244.
  3. Zaremba, S. (1907). L’equation biharmonique et une classe remarquable de fonctions fondamentales harmoniques. Bulletin International l’Academia des Sciences de Cracovie, pages 147-196.
  4. Zaremba, S. (1908). Sur le calcul numerique des fonctions demandees dan le probleme de dirichlet et le probleme hydrodynamique. Bulletin International l’Academia des Sciences de Cracovie, 125-195.
  5. Aronszajn, N. (1950). Theory of reproducing kernels. Trans. Amer. Math. Soc., 68, 337-404.
  6. Bergman, S. (1950). The kernel function and conformal mapping. American Mathematical Society, New York. Mohammadi, M., Mokhtari, R., and Isfahani, F.T. (2014). Solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space. Iranian Journal of Numerical Analysis and Optimization 4(1), 57-76.
  7. Cui, M., Lin, Y., and Yang, L. (2007). A new method of solving the coefficient inverse problem. Science in China Series A: Mathematics Apr., 50(4), 561-572.
  8. Xu, M.Q., and Lin, Y. (2016). Simplified reproducing kernel method for fractional differential equations with delay. Applied Mathematics Letters, 52, 156-161.
  9. Tang, Z.Q. and Geng, F.Z. (2016). Fitted reproducing kernel method for singularly perturbed delay initial value problems. Applied Mathematics and Computation, 284, 169-174.
  10. Fardi, M., Ghaziani, R.K., and Ghasemi, M. (2016). The reproducing kernel method for some variational problems depending on indefinite integrals. Mathematical Modelling and Analysis, 21(3), 412-429.
  11. Wahba, G. (1974). Regression design for some equivalence classes of kernels. The Annals of Statistics 2(5), 925-934.
  12. Nashed, M. Z., and Wahba, G. (1974). Regularization and approximation of linear operator equations in reproducing kernel spaces. Bulltetin of the American Mathematical Society,80(6), 1213-1218. Al e’damat, A.H. (2015). Analytical-numerical method for solving a class of two-point boundary value problems. International Journal of Mathematical Analysis 9(40), 1987-2002.
  13. Inc, M., and Akgül, A. (2014). Approximate solutions for MHD squeezing fluid flow by a novel method. Boundary Value Problems, 2014:18. Inc, M., Akgül, A., and Kilicman, A. (2013). Numerical solutions of the second-order one-dimensional telegraph equati