Computations with half-range Chebyshev polynomials
Journal of Computational and Applied Mathematics
A Fast Algorithm for Fourier Continuation
SIAM Journal on Scientific Computing
Approximation error in regularized SVD-based Fourier continuations
Applied Numerical Mathematics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Spatially Dispersionless, Unconditionally Stable FC---AD Solvers for Variable-Coefficient PDEs
Journal of Scientific Computing
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We obtain exponentially accurate Fourier series for nonperiodic functions on the interval $[-1,1]$ by extending these functions to periodic functions on a larger domain. The series may be evaluated, but not constructed, by means of the FFT. A complete convergence theory is given based on orthogonal polynomials that resemble Chebyshev polynomials of the first and second kinds. We analyze a previously proposed numerical method, which is unstable in theory but stable in practice. We propose a new numerical method that is stable both in theory and in practice.