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We develop the ultraspherical rectangular collocation (URC) method, a collocation implementation of the sparse ultraspherical method of Olver \& Townsend for two-point boundary-value problems.
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A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix
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Preconditioning rectangular spectral collocation
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A fast FFT-based discrete Legendre transform
N. Hale and A. Townsend · 2016
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Explicit construction of rectangular differentiation matrices
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Block Operators and Spectral Discretizations
J. L. Aurentz and L. N. Trefethen · 2017
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NIST Handbook of Mathematical Functions
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark · 2010
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J. Shen, T. Tang, and L.-L. Wang · 2011
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Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights
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A Fast and Well-Conditioned Spectral Method
S. Olver and A. Townsend · 2013
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Iteration-Free Computation of Gauss–Legendre Quadrature Nodes and Weights
I. Bogaert · 2014
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A. Townsend, T. Trogdon, and S. Olver · 2014
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L. N. Trefethen · 2019
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On symmetrizing the ultraspherical spectral method for self-adjoint problems
J. L. Aurentz and R. M. Slevinsky · 2020
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Fast algorithms using orthogonal polynomials
S. Olver, R. M. Slevinsky, and A. Townsend · 2020
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A universal Birkhoff pseudospectral method for solving boundary value problems
I. M. Ross, R. J. Proulx, and C. F. Borges · 2023
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On the convergence of spectral methods involving non-compact operators
T. Trogdon · 2023
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https://github.com/tomtrogdon/URCMethod.jl, 2024
T. Trogdon · 2024
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