Numerical simulation of telegraph and Cattaneo fractional‐type models using adaptive reproducing kernel framework
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6998
Abstract: In this article, a class of generalized telegraph and Cattaneo time‐fractional models along with Robin's initial‐boundary conditions is considered using the adaptive reproducing kernel framework. Accordingly, a relatively novel numerical treatment is introduced to investigate… read more here.
Keywords: reproducing kernel; kernel framework; adaptive reproducing; kernel ... See more keywords
Exponential-Reproducing-Kernel-Based Sparse Sampling Method for Finite Rate of Innovation Signal with Arbitrary Pulse Echo Position
Sign Up to like & getrecommendations! Published in 2019 at "Circuits, Systems, and Signal Processing"
DOI: 10.1007/s00034-018-0903-8
Abstract: AbstractAn exponential reproducing kernel (ERK) has been applied to data sparse sampling for finite rate of innovation (FRI) signals with the characteristic of flexible parameter setting in contrast to other sampling kernels. However, the signal… read more here.
Keywords: sparse sampling; pulse echo; reproducing kernel; exponential reproducing ... See more keywords
Construction and Monte Carlo Estimation of Wavelet Frames Generated by a Reproducing Kernel
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-021-09835-0
Abstract: We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as well… read more here.
Keywords: construction; monte carlo; reproducing kernel; kernel construction ... See more keywords
Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
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DOI: 10.1007/s00332-019-09574-z
Abstract: Transfer operators such as the Perron–Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project… read more here.
Keywords: eigendecompositions transfer; reproducing kernel; hilbert spaces; transfer operators ... See more keywords
Von Neumann stability analysis of the u–p reproducing kernel formulation for saturated porous media
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DOI: 10.1007/s00466-016-1349-0
Abstract: This paper introduces the von Neumann method to investigate the temporal stability of the displacement–pressure $$(u{-}p)$$(u-p) reproducing kernel formulation for saturated porous media. Both dynamic and quasi-static formulations are considered and the critical time steps… read more here.
Keywords: reproducing kernel; formulation saturated; size; kernel formulation ... See more keywords
A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method
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DOI: 10.1007/s10092-016-0196-x
Abstract: In this paper, a simple numerical method is proposed for solving singularly perturbed boundary layers problems exhibiting twin boundary layers. The method avoids the choice of fitted meshes. Firstly the original problem is transformed into… read more here.
Keywords: numerical method; singularly perturbed; reproducing kernel; boundary layers ... See more keywords
Hardy type inequaltiy for reproducing Kernel Hilbert space operators and related problems
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DOI: 10.1007/s11117-017-0489-6
Abstract: A Hardy type inequality for Reproducing Kernel Hilbert Space operators is proved. It is well known (see Halmos in A Hilbert space problem book. Springer, Berlin, 1982) the following power inequality for numerical radius of… read more here.
Keywords: left right; reproducing kernel; space; hilbert space ... See more keywords
Numerical Solutions of Fractional Systems of Two-Point BVPs by Using the Iterative Reproducing Kernel Algorithm
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DOI: 10.1007/s11253-018-1526-8
Abstract: We propose an efficient computational method, namely, the iterative reproducing kernel method for the approximate solution of fractional-order systems of two-point time boundary-value problems in the Caputo sense. Two extended inner-product spaces are constructed in… read more here.
Keywords: reproducing kernel; fractional systems; solution; iterative reproducing ... See more keywords
Revitalising Pedrick’s Approach to Reproducing Kernel Hilbert Spaces
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DOI: 10.1007/s11785-021-01091-w
Abstract: This short note has to make alive the overlooked work of Pedrick. It is rather a tour guide than exhausted examination of the content and intends to serve potential explorers of diverse kinds of reproducing… read more here.
Keywords: approach reproducing; reproducing kernel; hilbert spaces; revitalising pedrick ... See more keywords
Reproducing Kernel Method for Singularly Perturbed One-Dimensional Initial-Boundary Value Problems with Exponential Initial Layers
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DOI: 10.1007/s12346-017-0242-3
Abstract: In this paper, a meshless numerical method is proposed for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. The method is a combination of the domain decomposition method and the reproducing kernel method.… read more here.
Keywords: singularly perturbed; reproducing kernel; initial boundary; one dimensional ... See more keywords
An iterative approximation for time-fractional Cahn–Allen equation with reproducing kernel method
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DOI: 10.1007/s40314-018-0672-9
Abstract: In this article, we construct a novel iterative approach that depends on reproducing kernel method for Cahn–Allen equation with Caputo derivative. Representation of solution and convergence analysis are presented theoretically. Numerical results are given as… read more here.
Keywords: cahn allen; kernel method; reproducing kernel; allen equation ... See more keywords