The exponential accuracy of Fourier and Chebyshev differencing methods
SIAM Journal on Numerical Analysis
Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
Spectral methods in MatLab
Radial Basis Functions
Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation
SIAM Journal on Numerical Analysis
Asymptotic Fourier Coefficients for a C∞ Bell (Smoothed-“Top-Hat”) & the Fourier Extension Problem
Journal of Scientific Computing
Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data
Journal of Scientific Computing
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
New Quadrature Formulas from Conformal Maps
SIAM Journal on Numerical Analysis
A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations
Journal of Computational Physics
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We propose a pseudospectral hybrid algorithm to approximate the solution of partial differential equations (PDEs) with non-periodic boundary conditions. Most of the approximations are computed using Fourier expansions that can be efficiently obtained by fast Fourier transforms. To avoid the Gibbs phenomenon, super-Gaussian window functions are used in physical space. Near the boundaries, we use local polynomial approximations to correct the solution. We analyze the accuracy and eigenvalue stability of the method for several PDEs. The method compares favorably to traditional spectral methods, and numerical results indicate that for hyperbolic problems a time step restriction of O(1/N) is sufficient for stability.