Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 4Citation - Scopus: 4Recovering the Source Term for Parabolic Equation With Nonlocal Integral Condition(Wiley, 2021) Baleanu, Dumitru; Tran Thanh Phong; Le Dinh Long; Nguyen Duc Phuong; Thanh Phong, Tran; Duc Phuong, Nguyen; Dinh Long, Le; Long, Le Dinh; Phuong, Nguyen Duc; Phong, Tran ThanhThe main purpose of this article is to present a Tikhonov method to construct the source function f(x) of the parabolic diffusion equation. This problem is well known to be severely ill-posed. Therefore, regularization is required. The error estimates between the sought solution and the regularized solution are obtained under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. One numerical test illustrates that the proposed method is feasible and effective.Article Citation - WoS: 10Citation - Scopus: 10Recovering the Initial Value for a System of Nonlocal Diffusion Equations With Random Noise on the Measurements(Wiley, 2021) Tran Thanh Binh; Nguyen Duc Phuong; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Anh Triet; Binh, Tran Thanh; Phuong, Nguyen Duc; Can, Nguyen Huu; Triet, Nguyen AnhIn this work, we study the final value problem for a system of parabolic diffusion equations. In which, the final value functions are derived from a random model. This problem is severely ill-posed in the sense of Hadamard. By nonparametric estimation and truncation methods, we offer a new regularized solution. We also investigate an estimate of the error and a convergence rate between a mild solution and its regularized solutions. Finally, some numerical experiments are constructed to confirm the efficiency of the proposed method.Article Regularized Solution for Nonlinear Elliptic Equations With Random Discrete Data(Wiley, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Duc Phuong; Duc Phuong, Nguyen; Hoang Luc, Nguyen; Phuong, Nguyen Duc; Tuan, Nguyen Huy; Luc, Nguyen HoangThe aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.