Adaptive piecewise Poly-Sinc methods for function approximation

Khalil, Omar A.; El-Sharkawy, Hany A.; Youssef, Maha; Baumann, Gerd

doi:10.1016/j.apnum.2022.12.016

Applied Numerical Mathematics

2023

DOI: 10.1016/j.apnum.2022.12.016

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Adaptive piecewise Poly-Sinc methods for function approximation

Omar A. Khalil

Hany A. El-Sharkawy

Maha Youssef

et al.

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Cited by 2 publications

References 53 publications

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Interpolant Method in Analyzing the Laser-Induced Plasma Spectroscopy

Wu,

Zhou,

Luo

et al. 2024

Journal of Thermophysics and Heat Transfer

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A numerical algorithm that effectively solves the Abel integral equation in laser-induced plasma spectroscopy is introduced. The proposed algorithm utilizes a barycentric interpolation and a collocation method with second-kind Chebyshev nodes. This approach reduces the Abel integral equation to a linear system of equations, resulting in efficient approximate solutions. Analytical studies provide an error estimation for the proposed method, which further validates its effectiveness. Through numerical experiments, we demonstrate the ease of implementation and showcase the efficiency of the proposed method. Our results indicate that the proposed algorithm can provide valuable insight for researchers in the field of laser-induced plasma spectroscopy and beyond.

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Interpolant Method in Analyzing the Laser-Induced Plasma Spectroscopy

Wu,

Zhou,

Luo

et al. 2024

Journal of Thermophysics and Heat Transfer

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An h-Adaptive Poly-Sinc-Based Local Discontinuous Galerkin Method for Elliptic Partial Differential Equations

Khalil

Baumann

2023

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For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points. The adaptive approach, which uses Poly-Sinc interpolation to achieve a predetermined level of approximation accuracy, is a local discontinuous Galerkin method. We developed an a priori error estimate and demonstrated the exponential convergence of the Poly-Sinc-based discontinuous Galerkin technique, as well as the adaptive piecewise Poly-Sinc method, for function approximation and ordinary differential equations. In this paper, we demonstrate the exponential convergence in the number of iterations of the a priori error estimate derived for the local discontinuous Galerkin technique under the condition that a reliable estimate of the precise solution of the partial differential equation at the Sinc points exists. For the purpose of refining the computational domain, we employ a statistical strategy. The numerical results for elliptic PDEs with Dirichlet and mixed Neumann-Dirichlet boundary conditions are demonstrated to validate the adaptive greedy Poly-Sinc approach

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Adaptive piecewise Poly-Sinc methods for function approximation

Cited by 2 publications

References 53 publications

Interpolant Method in Analyzing the Laser-Induced Plasma Spectroscopy

Interpolant Method in Analyzing the Laser-Induced Plasma Spectroscopy

An h-Adaptive Poly-Sinc-Based Local Discontinuous Galerkin Method for Elliptic Partial Differential Equations

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