John P. Boyd

According to our database1, John P. Boyd authored at least 75 papers between 1988 and 2020.

Collaborative distances:
  • Dijkstra number2 of five.
  • Erdős number3 of four.

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Bibliography

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

Isospectral heterogeneous domains: A numerical study.
J. Comput. Phys. X, 2019

2018
Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides.
Comput. Phys. Commun., 2018

2017
All roots spectral methods: Constraints, floating point arithmetic and root exclusion.
Appl. Math. Lett., 2017

The Crane equation uuxx=-2: The general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities.
Appl. Math. Comput., 2017

New approximations to the principal real-valued branch of the Lambert W-function.
Adv. Comput. Math., 2017

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

A degree-increasing [N to N+1] homotopy for Chebyshev and Fourier spectral methods.
Appl. Math. Lett., 2016

2015
RBF-vortex methods for the barotropic vorticity equation on a sphere.
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

Chebyshev-Fourier spectral methods in bipolar coordinates.
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(-Ax4): Hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to exp(-Ax2n).
Appl. Math. Comput., 2014

Accurate calculation of the solutions to the Thomas-Fermi equations.
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 Review, 2013

The Nonconvergence of $$h$$ h -Refinement in Prolate Elements.
J. Sci. Comput., 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

One-point pseudospectral collocation for the one-dimensional Bratu equation.
Appl. Math. Comput., 2011

2010
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series.
J. Comput. Phys., 2010

Error saturation in Gaussian radial basis functions on a finite interval.
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

Asymptotic coefficients for Gaussian radial basis function interpolants.
Appl. Math. Comput., 2010

The Legendre-Burgers equation: When artificial dissipation fails.
Appl. Math. Comput., 2010

2009
Three ways to solve the Poisson equation on a sphere with Gaussian forcing.
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 Review, 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 C 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 Review, 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.
Appl. Math. Comput., 2005

2003
Large mode number eigenvalues of the prolate spheroidal differential equation.
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
The Blasius Function in the Complex Plane.
Experimental Mathematics, 1999

1993
Chebyshev and Legendre Spectral Methods in Algebraic Manipulation Languages.
J. Symb. Comput., 1993

1990
An Introduction to the Numerical Analysis of Spectral Methods (Bertrand Mercier).
SIAM Review, 1990

1988
Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval.
J. Sci. Comput., 1988


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