John P. Boyd
Orcid: 0000-0003-3737-9715Affiliations:
- University of Michigan, Department of Atmospheric, Oceanic & Space Science, Ann Arbor, MI, USA
According to our database1,
John P. Boyd
authored at least 80 papers
between 1988 and 2023.
Collaborative distances:
Collaborative distances:
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Online presence:
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on zbmath.org
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on orcid.org
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on id.loc.gov
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on d-nb.info
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Bibliography
2023
Using parity to accelerate Hermite function computations: Zeros of truncated Hermite series, Gaussian quadrature and Clenshaw summation.
Math. Comput. Simul., May, 2023
2022
Exact solutions to a nonlinear partial differential equation: The Product-of-Curvatures Poisson (uxxuyy=1).
J. Comput. Appl. Math., 2022
2021
Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases.
CoRR, 2021
2020
Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case.
J. Sci. Comput., 2020
2019
When integration sparsification fails: Banded Galerkin discretizations for Hermite functions, rational Chebyshev functions and sinh-mapped Fourier functions on an infinite domain, and Chebyshev methods for solutions with C∞ endpoint singularities.
Math. Comput. Simul., 2019
2018
Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides.
Comput. Phys. Commun., 2018
2017
Convergent Power Series for Boundary Value Problems and Eigenproblems with Application to Atmospheric and Oceanic Tides.
Am. Math. Mon., 2017
All roots spectral methods: Constraints, floating point arithmetic and root exclusion.
Appl. Math. Lett., 2017
The Crane equation uu<sub>xx</sub>=-2: The general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities.
Appl. Math. Comput., 2017
Adv. Comput. Math., 2017
2016
Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis.
Am. Math. Mon., 2016
Tracing Multiple Solution Branches for Nonlinear Ordinary Differential Equations: Chebyshev and Fourier Spectral Methods and a Degree-Increasing Spectral Homotopy [DISH].
J. Sci. Comput., 2016
High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences.
J. Comput. Phys., 2016
Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: Restrictions and two improvements.
J. Comput. Appl. Math., 2016
Five themes in Chebyshev spectral methods applied to the regularized Charney eigenproblem: Extra numerical boundary conditions, a boundary-layer-resolving change of coordinate, parameterizing a curve which is singular at an endpoint, extending the tau method to log-and-polynomials and finding the roots of a polynomial-and-log approximation.
Comput. Math. Appl., 2016
Appl. Math. Lett., 2016
2015
J. Comput. Phys., 2015
Approximation on non-tensor domains including squircles, Part III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids.
J. Comput. Phys., 2015
Adaptive radial basis function and Hermite function pseudospectral methods for computing eigenvalues of the prolate spheroidal wave equation for very large bandwidth parameter.
J. Comput. Phys., 2015
Modal preconditioning of Galerkin spectral methods: Dual bookkeeping for the Delves-Freeman iteration.
J. Comput. Phys., 2015
Four ways to compute the inverse of the complete elliptic integral of the first kind.
Comput. Phys. Commun., 2015
Spectral methods in non-tensor geometry, Part II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains.
Appl. Math. Comput., 2015
A Fourier error analysis for radial basis functions and the Discrete Singular Convolution on an infinite uniform grid, Part 1: Error theorem and diffusion in Fourier space.
Appl. Math. Comput., 2015
2014
The Relationships Between Chebyshev, Legendre and Jacobi Polynomials: The Generic Superiority of Chebyshev Polynomials and Three Important Exceptions.
J. Sci. Comput., 2014
Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I.
J. Comput. Phys., 2014
The Fourier Transform of the quartic Gaussian exp(-Ax<sup>4</sup>): Hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to exp(-Ax<sup>2n</sup>).
Appl. Math. Comput., 2014
Appl. Math. Comput., 2014
Solving Transcendental Equations - the Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles.
SIAM, ISBN: 978-1-611-97351-8, 2014
2013
Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix.
SIAM Rev., 2013
A comparison of companion matrix methods to find roots of a trigonometric polynomial.
J. Comput. Phys., 2013
Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods.
J. Comput. Appl. Math., 2013
Quartic Gaussian and Inverse-Quartic Gaussian radial basis functions: The importance of a nonnegative Fourier transform.
Comput. Math. Appl., 2013
Hermite function interpolation on a finite uniform grid: Defeating the Runge phenomenon and replacing radial basis functions.
Appl. Math. Lett., 2013
A Fourier error analysis for radial basis functions on an infinite uniform grid. Part 2: Spectral-plus is special.
Appl. Math. Comput., 2013
2012
Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions.
J. Comput. Phys., 2012
Parity symmetry with respect to both x=0 and x=L requires periodicity with period 4L: Connections between computer graphics, group theory and spectral methods for solving partial differential equations.
Appl. Math. Comput., 2012
Computing the real roots of a Fourier series-plus-linear-polynomial: A Chebyshev companion matrix approach.
Appl. Math. Comput., 2012
Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind.
Appl. Math. Comput., 2012
2011
Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions.
J. Comput. Phys., 2011
The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): Asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid.
J. Comput. Phys., 2011
New series for the cosine lemniscate function and the polynomialization of the lemniscate integral.
J. Comput. Appl. Math., 2011
Appl. Math. Comput., 2011
2010
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series.
J. Comput. Phys., 2010
J. Comput. Appl. Math., 2010
Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval.
Comput. Math. Appl., 2010
Appl. Math. Comput., 2010
Appl. Math. Comput., 2010
2009
J. Comput. Phys., 2009
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n.
J. Comput. Phys., 2009
Divergence (Runge Phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock-Chebyshev subset interpolation.
Appl. Math. Comput., 2009
An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice.
Appl. Math. Comput., 2009
2008
The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems.
SIAM Rev., 2008
Evaluating of Dawson's Integral by solving its differential equation using orthogonal rational Chebyshev functions.
Appl. Math. Comput., 2008
Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials.
Appl. Math. Comput., 2008
2007
Why Newton's method is hard for travelling waves: Small denominators, KAM theory, Arnold's linear Fourier problem, non-uniqueness, constraints and erratic failure.
Math. Comput. Simul., 2007
Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries.
Comput. Math. Appl., 2007
Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid.
Appl. Math. Lett., 2007
A test, based on conversion to the Bernstein polynomial basis, for an interval to be free of zeros applicable to polynomials in Chebyshev form and to transcendental functions approximated by Chebyshev series.
Appl. Math. Comput., 2007
2006
Asymptotic Fourier Coefficients for a <i>C</i> infinity Bell (Smoothed-"Top-Hat") & the Fourier Extension Problem.
J. Sci. Comput., 2006
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences.
J. Comput. Phys., 2006
Rootfinding through global Newton iteration and Chebyshev polynomials for the amplitude of an electronic oscillator.
Appl. Math. Comput., 2006
Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves.
Appl. Math. Comput., 2006
Fourier pseudospectral method with Kepler mapping for travelling waves with discontinuous slope: Application to corner waves of the Ostrovsky-Hunter equation and equatorial Kelvin waves in the four-mode approximation.
Appl. Math. Comput., 2006
2005
Algorithm 840: computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions - prolate elements.
ACM Trans. Math. Softw., 2005
Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge.
SIAM Rev., 2005
Chebyshev solution of the nearly-singular one-dimensional Helmholtz equation and related singular perturbation equations: multiple scale series and the boundary layer rule-of-thumb.
Numer. Algorithms, 2005
The cnoidal wave/corner wave/breaking wave scenario: A one-sided infinite-dimension bifurcation.
Math. Comput. Simul., 2005
Fourier embedded domain methods: extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and C<sup>∞</sup>.
Appl. Math. Comput., 2005
2003
Appl. Math. Comput., 2003
Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation.
Appl. Math. Comput., 2003
2002
Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding.
SIAM J. Numer. Anal., 2002
Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude.
Appl. Math. Comput., 2002
2001
Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm.
Appl. Math. Lett., 2001
1999
1993
J. Symb. Comput., 1993
1990
SIAM Rev., 1990
1988
Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval.
J. Sci. Comput., 1988