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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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Ain Shams Engineering Journal, 2018 In this article, we introduce a novel numerical scheme, the iterative reproducing kernel method (IRKM), for providing numerical approximate solutions of a certain class of time-fractional boundary value problem within favorable aspects of the reproducing
Mohammed Al-Smadi
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Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate [PDF]
Computational and Applied Mathematics, 2019 Onur Saldır +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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Numerical Solution of Fractional Bratu Type Equations with Legendre Reproducing Kernel Method [PDF]
International Journal of Applied and Computational Mathematics, 2018 In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense.
Mehmet Giyas Sakar +2 more
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Open Physics, 2016 In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model.
Akgül Ali +3 more
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Thermal Science, 2021 This paper structures some new reproductive kernel spaces based on Legendre polynomials to solve time variable order fractional advection-reaction-diffusion equations. Some examples are given to show the effectiveness and reliability of the method.
Dandan Dai +3 more
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Fractal and Fractional, 2022 Fractional-order calculus has become a useful mathematical framework to describe the complex super-diffusive process; however, numerical solutions of the two-sided space-fractional super-diffusive model with variable coefficients are difficult to obtain,
Zhiyuan Li +3 more
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