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Reproducing Kernel Method with Global Derivative
Journal of Function Spaces, 2023 Ordinary differential equations describe several phenomena in different fields of engineering and physics. Our aim is to use the reproducing kernel Hilbert space method (RKHSM) to find a solution to some ordinary differential equations (ODEs) that are ...
Nourhane Attia +2 more
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A point collocation method based on reproducing kernel approximations [PDF]
International Journal for Numerical Methods in Engineering, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. R. Aluru
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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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Numerical solution of potential problems using radial basis reproducing kernel particle method
Results in Physics, 2019 The paper presents the radial basis reproducing kernel particle method (RRKPM) for potential problems. The proposed RRKPM can eliminate the negative effect of different reproducing kernel functions (RKF) on computational stability and accuracy.
Hongfen Gao, Gaofeng Wei
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Reproducing Kernel Method for Fractional Riccati Differential Equations [PDF]
Abstract and Applied Analysis, 2014 This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique.
X. Y. Li, B. Y. Wu, R. T. Wang
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A new application of the Legendre reproducing kernel method
AIMS Mathematics, 2022 In 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.
Mohammad Reza Foroutan +4 more
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Numerical technique for solving physical models using reproducing kernel Hilbert space method with purely integral conditions [PDF]
Boundary Value ProblemsIn this work, we investigate the Klein–Gordon equation, a physical problem, using the reproducing kernel Hilbert space method (RKHSM). The analytical solution is expressed as a series within the reproducing kernel Hilbert space (RKHS).
Hadjer Zerouali +6 more
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Reproducing kernel particle method and its modification [PDF]
Mathematica Bohemica, 2010 Meshless methods have become an effective tool for solving problems from engineering practice in last years. They have been successfully applied to problems in solid and fluid mechanics. One of their advantages is that they do not require any explicit mesh in computation.
Vratislava Mošová
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Interpolation-based reproducing kernel particle method
Computer Methods in Applied Mechanics and EngineeringMeshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology changes. RKPM shape functions and their derivatives cannot be accurately integrated with the Gauss-quadrature methods ...
Jennifer E. Fromm +2 more
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A new kernel method for the uniform approximation in reproducing kernel Hilbert spaces
Applied Mathematics LettersWe are concerned with the uniform approximation of functions of a generic reproducing kernel Hilbert space (RKHS). In this general context, classical approximations are given by Fourier orthogonal projections (if we know the Fourier coefficients) and their discrete versions (if we know the function values on well-distributed nodes).
Woula Themistoclakis, Marc Van Barel
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