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investigating nonlinear fractional systems: reproducing kernel Hilbert space method
Optical and Quantum Electronics, 2023Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia [221412044]
Attia, Nourhane +2 more
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On Solutions of Biological Models Using Reproducing Kernel Hilbert Space Method
2023Differential equations (DEs, for short) are becoming more and more indispensable for modeling real-life problems. Modeling and then analyzing these DEs help scientists to understand and make predictions about the system that they want to analyze. And this is possible only in one case when their solutions are available.
Attia, Nourhane, Akgül, Ali
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Reproducing Kernel Hilbert Space Method for Solving Bratu’s Problem
Bulletin of the Malaysian Mathematical Sciences Society, 2014In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order Bratu’s differential equation. Convergence analysis of presented method is discussed. The numerical approximations to the exact solution are computed and compared with other existing methods.
Mustafa Inc, Ali Akgül, Fazhan Geng
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Reproducing kernel Hilbert space method for optimal interpolation of potential field data
IEEE Transactions on Image Processing, 1998The RKHS-based optimal image interpolation method, presented by Chen and de Figueiredo (1993), is applied to scattered potential field measurements. The RKHS which admits only interpolants consistent with Laplace's equation is defined and its kernel, derived.
J. Maltz, A.J. Willis, R. De Mello Koch
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Solutions of Integral Equations by Reproducing Kernel Hilbert Space Method
2021The theory of reproducing kernels was considered for the first time at the beginning of the 20th century by Zaremba. Reproducing kernel theory has valuable implementations in numerical analysis, differential equations, probability and statistics.
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Reproducing kernel Hilbert space method for nonlinear boundary‐value problems
Mathematical Methods in the Applied Sciences, 2018Reproducing kernel Hilbert space method is given for nonlinear boundary‐value problems in this paper. Applying this technique, we establish a new algorithm to approximate the solution of such nonlinear boundary‐value problems. This technique does not need any background mesh and can easily be applied.
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The Backus-Gilbert method for signals in reproducing kernel Hilbert spaces and wavelet subspaces
Inverse Problems, 1994The Backus-Gilbert method for signal recovery from moments of a signal, when moments of a function and related kernel functions are known, is considered when in addition the signal to be recovered is known to be in certain wavelet subspaces. In these days of computers inversion processes have become important in numerical analysis also, see for example
M Z Nashed, Xiang-Gen Xia
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Mathematical Methods in the Applied Sciences, 2020
This research work is concerned with the new numerical solutions of some essential fractional cancer tumor models, which are investigated by using reproducing kernel Hilbert space method (RKHSM). The most valuable advantage of the RKHSM is its ease of use and its quick calculation to obtain the numerical solutions of the considered problem. We make use
Nourhane Attia +3 more
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This research work is concerned with the new numerical solutions of some essential fractional cancer tumor models, which are investigated by using reproducing kernel Hilbert space method (RKHSM). The most valuable advantage of the RKHSM is its ease of use and its quick calculation to obtain the numerical solutions of the considered problem. We make use
Nourhane Attia +3 more
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Solving Higher-Order Fractional Differential Equations by Reproducing Kernel Hilbert Space Method
Journal of Advanced Physics, 2018In this work, we apply reproducing kernel Hilbert space method to investigate higher-order fractional differential equations. We used a bounded linear operator and some useful reproducing kernel functions to get accurate results. We present an experiment to prove how real our theory can be performed in the applications.
Akgul, Esra Karatas +2 more
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Reproducing Kernel Hilbert Space Methods to Reduce Pulse Compression Sidelobes
2007Since the development of pulse compression in the mid- 1950's the concept has become an indispensable feature of modern radar systems. A matched filter is used on reception to maximize the signal to noise ratio of the received signal. The actual waveforms that are transmitted are chosen to have an autocorrelation function with a narrow peak at zero ...
B.J. van Wyk, M.A. van Wyk, Jaco Jordaan
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