Asymptotic Fourier coefficients for a \(C^\infty\) bell (smoothed-``top-hat) \& the Fourier extension problem
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Publication:858028
DOI10.1007/s10915-005-9010-7zbMath1105.65129OpenAlexW2117804954MaRDI QIDQ858028
Publication date: 5 January 2007
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-005-9010-7
Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)
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Cites Work
- Parallel implementation of non-linear evolution problems using parabolic domain decomposition
- Asymptotic coefficients of Hermite function series
- Construction of Lighthill's unitary functions: The imbricate series of unity
- The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
- An adaptive algorithm for spectral computations on unbounded domains
- A new parallel solver for the nonperiodic incompressible Navier-Stokes equations with a Fourier method: Application to frontal polymerization
- Two-dimensional parallel solver for the solution of Navier--Stokes equations with constant and variable coefficients using ADI on cells
- Vlasov simulations using velocity-scaled Hermite representations
- From local cosine bases to global harmonics
- Mixed spectral-boundary element embedding algorithms for the Navier-Stokes equations in the vorticity-stream function formulation
- Spectral multidomain technique with local Fourier basis
- The rate of convergence of Fourier coefficients for entire functions of infinite order with application to the Weideman-Cloot Sinh-mapping for pseudospectral computations on an infinite interval
- Biorthogonal smooth local trigonometric bases
- On a fast direct elliptic solver by a modified Fourier method
- Efficient computation of oscillatory integrals via adaptive multiscale local Fourier bases
- A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
- Fourier embedded domain methods: Extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and \(C^{\infty}\)
- Orthogonal rational functions on a semi-infinite interval
- Spectral methods using rational basis functions on an infinite interval
- A spectral embedding method applied to the advection-diffusion equation
- Multidomain local Fourier method for PDEs in complex geometries
- Asymptotic Chebyshev coefficients for two functions with very rapidly or very slowly divergent power series about one endpoint
- Optimized local trigonometric bases
- New Directions in Solitons and Nonlinear Periodic Waves: Polycnoidal Waves, Imbricated Solitons, Weakly Nonlocal Solitary Waves, and Numerical Boundary Value Algorithms
- Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers
- The Fringe Region Technique and the Fourier Method Used in the Direct Numerical Simulation of Spatially Evolving Viscous Flows
- Spectrally Accurate Solution of Nonperiodic Differential Equations by the Fourier--Gegenbauer Method
- Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
- On Some Applications of the Superposition Principle with Fourier Basis
- The Hermite Spectral Method for Gaussian-Type Functions
- Some Estimates of the Coefficients in the Chebyshev Series Expansion of a Function
- Truncation Errors in Two Chebyshev Series Approximations
- On the Convergence of the Chebyshev Series for Functions Possessing a Singularity in the Range of Representation
- Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm
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