Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Antenna Synthesis by Levin's Method Using Reproducing Kernel Functions(Applied Computational Electromagnetics Soc, 2023) Sener, GokerAn antenna synthesis application is presented by solving a highly oscillatory Fourier integral using a stable and accurate Levin's algorithm. In antenna synthesis, the current distribution is obtained by the inverse Fourier integral of the antenna radiation pattern. Since this integral is highly oscillatory, the Levin method can be used for its solution. However, when the number of nodes or the frequency increases, the Levin method becomes unstable and ineffective due to the large condition number of the interpolation matrix. Thus, an improved scheme of the method is used in an antenna synthesis application in which reproducing kernel functions are used as the basis of the approximation function. The accuracy of the new method is verified by a log-periodic antenna example. The error and stability analysis results show that the new method is more stable and accurate than other well-known kernels, especially for a large number of nodes.Article Citation - WoS: 2Citation - Scopus: 4A New Application of the Legendre Reproducing Kernel Method(Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad RezaIn this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.Article Citation - WoS: 7Citation - Scopus: 8Representation for the Reproducing Kernel Hilbert Space Method for a Nonlinear System(Hacettepe Univ, Fac Sci, 2019) Akgul, Ali; Khan, Yasir; Baleanu, Dumitru; Akgul, Esra Karatas; Karatas Akgül, EsraWe apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.Article Citation - WoS: 14Citation - Scopus: 13New Method for Investigating the Density-Dependent Diffusion Nagumo Equation(Vinca inst Nuclear Sci, 2018) Hashemi, Mir Sajjad; Inc, Mustafa; Baleanu, Dumitru; Khan, Hasib; Akgul, AliWe apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.Article Citation - WoS: 4Citation - Scopus: 6New Numerical Method for Solving Tenth Order Boundary Value Problems(Mdpi, 2018) Akgul, Esra Karatas; Baleanu, Dumitru; Inc, Mustafa; Akgul, AliIn this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.Article Citation - WoS: 15Citation - Scopus: 16Solving the Lane-Emden Equation Within a Reproducing Kernel Method and Group Preserving Scheme(Mdpi, 2017) Akgul, Ali; Inc, Mustafa; Mustafa, Idrees Sedeeq; Baleanu, Dumitru; Hashemi, Mir SajjadWe apply the reproducing kernel method and group preserving scheme for investigating the Lane-Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These approximations demonstrate the preciseness of the investigated techniques.