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

Esra Karatas Akgül

Abstract


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


Keywords


Reproducing kernel functions, inverse problem for the kinetic equation, reproducing kernel Hilbert space.

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References


Golgeleyen, F., and Amirov, A. (2011). On the approximate solution of a coefficient inverse problem for the kinetic equation. Math. Commun. 16, 283-298.

Perthame, B. (2014). Mathematical tools for kinetic equations, Bull. Amer. Math. Soc. 41, 205-244.

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.

Zaremba, S. (1908). Sur le calcul numerique des fonctions demandees dan le probleme de dirichlet etle probleme hydrodynamique. Bulletin International l’Academia des Sciences de Cracovie, 125-195.

Aronszajn, N. (1950). Theory of reproducing kernels. Trans. Amer. Math. Soc., 68, 337-404.

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.

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.

Xu, M.Q., and Lin, Y. (2016). Simplified reproducing kernel method for fractional differential equations with delay. Applied Mathematics Letters, 52, 156-161.

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.

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.

Wahba, G. (1974). Regression design for some equivalence classes of kernels. The Annals of Statistics 2(5), 925-934.

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.

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 equation based on reproducing kernel hilbert space method. Abstract and Applied Analysis, Article ID 768963, 13 pages.

Akgül, A., and Kilicman, A. (2015). Solving delay differential equations by an accurate method with interpolation. Abstract and Applied Analysis, Article ID 676939, 7 pages.

Akgül, A. (2015). New reproducing kernel functions. Mathematical Problems in Engineering, Article ID 158134, 10 pages.

Inc., M., and Akgül, A. (2014). Numerical solution of seventh-order boundary value problems by a novel method. Abstract and Applied Analysis, Article ID 745287, 9 pages.

Boutarfa, B., Akgül, A., and Inc, M. (2017). New approach for the Fornberg-Whitham type equations. Journal of Computational and Applied Mathematics, 312, 13-26.

Sakar, M.G., Akgül, A., and Baleanu, D. (2017). On solutions of fractional Riccati differential equations. Advances in Difference Equations. 2017:39.

Akgül, A., and Grow, D. Existence of solutions to the Telegraph Equation in binary reproducing kernel Hilbert spaces, , Submitted




DOI: http://dx.doi.org/10.11121/ijocta.01.2018.00568

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