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.
Highlights
IntroductionWe consider the problem of obtaining (f, σ) in Ω from the following equation [1]: Kinetic theory emerged with Maxwell and Boltzmann, Hilbert, Enskog, Chapman, Vlasov, and
We consider the problem of obtaining (f, σ) in Ω from the following equation [1]: Kinetic theory emerged with Maxwell and Boltzmann, Hilbert, Enskog, Chapman, Vlasov, andMv(x, v)fx(x, v) − Mx(x, v)fv(x, v) (1)Grad
We found the main reproducing kernel function for the problem
Summary
We consider the problem of obtaining (f, σ) in Ω from the following equation [1]: Kinetic theory emerged with Maxwell and Boltzmann, Hilbert, Enskog, Chapman, Vlasov, and. Mann modeled the operation, endowed a common representation of a dilute gas as particles In this work, the reproducing kernel functions for undergoing collisions and with free motion be- solving a coefficient inverse problem (IP) for the tween collisions, and he found the famous equa- KE are given. Reproducing kernel method of solving the coefficient inverse problem [8]. Tang et al applied fitted reproducing kernel method for singularly perturbed delay initial value problems [10]. Al e’damat applied analytical-numerical method for solving a class of two-point boundary value problems [14]. For more details see [15,16,17,18,19,20,21]
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