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Solutions of nonlinear systems by reproducing kernel method [PDF]
The Journal of Nonlinear Sciences and Applications, 2017 ...
Akgul, Ali +4 more
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Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral [PDF]
Journal of Applied Mathematics, 2012 We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains
Er Gao, Songhe Song, Xinjian Zhang
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A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method [PDF]
Abstract and Applied Analysis, 2013 We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space.
Mustafa Inc, Ali Akgül, Adem Kiliçman
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Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method [PDF]
Journal of Applied Mechanics, 1997 The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The
Chen, Y., Liu, W.K., Uras, R.A.
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Journal of Taibah University for Science, 2019 Reproducing kernel Hilbert space method is given for the solution of generalized Kuramoto–Sivashinsky equation. Reproducing kernel functions are obtained to get the solution of the generalized Kuramoto–Sivashinsky equation.
Ali Akgül, Ebenezer Bonyah
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Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method [PDF]
Abstract and Applied Analysis, 2013 A numerical technique based on reproducing kernel methods for the exact solution of linear Volterra integral equations system of the second kind is given.
Li-Hong Yang +2 more
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Reproducing kernel functions for the generalized Kuramoto-Sivashinsky equation
ITM Web of Conferences, 2018 Reproducing kernel functions are obtained for the solution of generalized Kuramoto–Sivashinsky (GKS) equation in this paper. These reproducing kernel functions are valuable in the reproducing kernel Hilbert space method.
Akgül Ali +3 more
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Explicit Solution of Telegraph Equation Based on Reproducing Kernel Method [PDF]
Journal of Function Spaces and Applications, 2012 We propose a reproducing kernel method for solving the telegraph equation with initial conditions based on the reproducing kernel theory. The exact solution is represented in the form of series, and some numerical examples have been studied in order to ...
Mustafa Inc, Ali Akgül, Adem Kiliçman
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Alexandria Engineering Journal, 2020 In this paper, on the basis of the reproducing kernel functions, a novel meshless algorithm is explored for fractional advection–diffusion-reaction equations (ADREs) with Caputo time variable order.
Xiuying Li, Boying Wu
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Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators [PDF]
Advances in Mathematical Physics, 2014 A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of ...
Banan Maayah +3 more
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