John P. Boyd

Publication Activity (10 Years)

Years Active: 1988-2023
Publications (10 Years): 25

Top Topics

Basis Functions

Eigendecomposition

Spectral Methods

Top Venues

J. Comput. Phys.

Appl. Math. Comput.

J. Sci. Comput.

Appl. Math. Lett.

Publications

John P. Boyd
Using parity to accelerate Hermite function computations: Zeros of truncated Hermite series, Gaussian quadrature and Clenshaw summation. Math. Comput. Simul. 207 (2023)
Xiaolong Zhang, John P. Boyd
Exact solutions to a nonlinear partial differential equation: The Product-of-Curvatures Poisson (uxxuyy=1). J. Comput. Appl. Math. 406 (2022)
Xiaolong Zhang, John P. Boyd
Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases. CoRR (2021)
Xiaolong Zhang, John P. Boyd
Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case. J. Sci. Comput. 82 (2) (2020)
Zhu Huang, John P. Boyd
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. 160 (2019)
Paolo Amore, John P. Boyd, Natalia Tene Sandoval
Isospectral heterogeneous domains: A numerical study. J. Comput. Phys. X 1 (2019)
John P. Boyd, Paolo Amore, Francisco M. Fernández
Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides. Comput. Phys. Commun. 224 (2018)
John P. Boyd, Houjun Wang
Convergent Power Series for Boundary Value Problems and Eigenproblems with Application to Atmospheric and Oceanic Tides. Am. Math. Mon. 124 (4) (2017)
John P. Boyd, Calin-Ioan Gheorghiu
All roots spectral methods: Constraints, floating point arithmetic and root exclusion. Appl. Math. Lett. 67 (2017)
Roberto Iacono, John P. Boyd
New approximations to the principal real-valued branch of the Lambert W-function. Adv. Comput. Math. 43 (6) (2017)
John P. Boyd
=-2: The general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities. Appl. Math. Comput. 301 (2017)
John P. Boyd
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. 71 (6) (2016)
John P. Boyd
Tracing Multiple Solution Branches for Nonlinear Ordinary Differential Equations: Chebyshev and Fourier Spectral Methods and a Degree-Increasing Spectral Homotopy [DISH]. J. Sci. Comput. 69 (3) (2016)
John P. Boyd
Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis. Am. Math. Mon. 123 (3) (2016)
Zhu Huang, John P. Boyd
Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: Restrictions and two improvements. J. Comput. Appl. Math. 302 (2016)
John P. Boyd
A degree-increasing [N to N+1] homotopy for Chebyshev and Fourier spectral methods. Appl. Math. Lett. 57 (2016)
Paolo Amore, John P. Boyd, Francisco M. Fernández, Boris Rösler
High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. J. Comput. Phys. 312 (2016)
Jianping Xiao, Lei Wang, John P. Boyd
RBF-vortex methods for the barotropic vorticity equation on a sphere. J. Comput. Phys. 285 (2015)
Zhu Huang, John P. Boyd
Chebyshev-Fourier spectral methods in bipolar coordinates. J. Comput. Phys. 295 (2015)
Shan Li, John P. Boyd
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. 269 (2015)
Zhu Huang, Jianping Xiao, John P. Boyd
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. 281 (2015)
John P. Boyd
Four ways to compute the inverse of the complete elliptic integral of the first kind. Comput. Phys. Commun. 196 (2015)
Zhu Huang, John P. Boyd
Modal preconditioning of Galerkin spectral methods: Dual bookkeeping for the Delves-Freeman iteration. J. Comput. Phys. 300 (2015)
Shan Li, John P. Boyd
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. 281 (2015)
John P. Boyd
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. 264 (2015)
Shan Li, John P. Boyd
Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I. J. Comput. Phys. 258 (2014)
John P. Boyd, Rolfe Petschek
The Relationships Between Chebyshev, Legendre and Jacobi Polynomials: The Generic Superiority of Chebyshev Polynomials and Three Important Exceptions. J. Sci. Comput. 59 (1) (2014)
Paolo Amore, John P. Boyd, Francisco M. Fernández
Accurate calculation of the solutions to the Thomas-Fermi equations. Appl. Math. Comput. 232 (2014)
John P. Boyd
). Appl. Math. Comput. 241 (2014)
John P. Boyd
Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix. SIAM Rev. 55 (2) (2013)
John P. Boyd, Philip W. McCauley
Quartic Gaussian and Inverse-Quartic Gaussian radial basis functions: The importance of a nonnegative Fourier transform. Comput. Math. Appl. 65 (1) (2013)
John P. Boyd
A comparison of companion matrix methods to find roots of a trigonometric polynomial. J. Comput. Phys. 246 (2013)
John P. Boyd, Gregor Gassner, Burhan A. Sadiq
The Nonconvergence of $$h$$ h -Refinement in Prolate Elements. J. Sci. Comput. 57 (2) (2013)
John P. Boyd
Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods. J. Comput. Appl. Math. 244 (2013)
John P. Boyd
A Fourier error analysis for radial basis functions on an infinite uniform grid. Part 2: Spectral-plus is special. Appl. Math. Comput. 225 (2013)
John P. Boyd, Luis F. Alfaro
Hermite function interpolation on a finite uniform grid: Defeating the Runge phenomenon and replacing radial basis functions. Appl. Math. Lett. 26 (10) (2013)
John P. Boyd, Zhengjie Xu
Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions. J. Comput. Phys. 231 (4) (2012)
John P. Boyd, Burhan A. Sadiq
Computing the real roots of a Fourier series-plus-linear-polynomial: A Chebyshev companion matrix approach. Appl. Math. Comput. 219 (3) (2012)
John P. Boyd, Yang (Chris) Xiu
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. 219 (8) (2012)
John P. Boyd
Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind. Appl. Math. Comput. 218 (13) (2012)
John P. Boyd, Fu Yu
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. 230 (4) (2011)
John P. Boyd
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. 230 (4) (2011)
John P. Boyd
New series for the cosine lemniscate function and the polynomialization of the lemniscate integral. J. Comput. Appl. Math. 235 (8) (2011)
John P. Boyd
One-point pseudospectral collocation for the one-dimensional Bratu equation. Appl. Math. Comput. 217 (12) (2011)
John P. Boyd
The Legendre-Burgers equation: When artificial dissipation fails. Appl. Math. Comput. 217 (5) (2010)
John P. Boyd
Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval. Comput. Math. Appl. 60 (12) (2010)
John P. Boyd, Lei Wang
Asymptotic coefficients for Gaussian radial basis function interpolants. Appl. Math. Comput. 216 (8) (2010)
John P. Boyd
Error saturation in Gaussian radial basis functions on a finite interval. J. Comput. Appl. Math. 234 (5) (2010)
John P. Boyd
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series. J. Comput. Phys. 229 (4) (2010)
John P. Boyd, Cheng Zhou
Three ways to solve the Poisson equation on a sphere with Gaussian forcing. J. Comput. Phys. 228 (13) (2009)
John P. Boyd, Lei Wang
An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice. Appl. Math. Comput. 215 (6) (2009)
John P. Boyd
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n. J. Comput. Phys. 228 (5) (2009)
John P. Boyd, Fei Xu
Divergence (Runge Phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock-Chebyshev subset interpolation. Appl. Math. Comput. 210 (1) (2009)
John P. Boyd
Evaluating of Dawson's Integral by solving its differential equation using orthogonal rational Chebyshev functions. Appl. Math. Comput. 204 (2) (2008)
John P. Boyd
The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems. SIAM Rev. 50 (4) (2008)
John P. Boyd
Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials. Appl. Math. Comput. 198 (2) (2008)
John P. Boyd
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. 188 (2) (2007)
John P. Boyd
Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid. Appl. Math. Lett. 20 (9) (2007)
John P. Boyd
Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries. Comput. Math. Appl. 54 (3) (2007)
John P. Boyd
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. 74 (2-3) (2007)
John P. Boyd
infinity Bell (Smoothed-"Top-Hat") & the Fourier Extension Problem. J. Sci. Comput. 29 (1) (2006)
John P. Boyd
Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Appl. Math. Comput. 174 (2) (2006)
John P. Boyd, Robert M. Visser
Rootfinding through global Newton iteration and Chebyshev polynomials for the amplitude of an electronic oscillator. Appl. Math. Comput. 182 (1) (2006)
John P. Boyd
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. 177 (1) (2006)
John P. Boyd
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. J. Comput. Phys. 214 (2) (2006)
John P. Boyd
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 38 (1-3) (2005)
John P. Boyd
. Appl. Math. Comput. 161 (2) (2005)
John P. Boyd
Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge. SIAM Rev. 47 (3) (2005)
John P. Boyd
The cnoidal wave/corner wave/breaking wave scenario: A one-sided infinite-dimension bifurcation. Math. Comput. Simul. 69 (3-4) (2005)
John P. Boyd
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. 31 (1) (2005)
John P. Boyd
Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Appl. Math. Comput. 143 (2-3) (2003)
John P. Boyd
Large mode number eigenvalues of the prolate spheroidal differential equation. Appl. Math. Comput. 145 (2-3) (2003)
John P. Boyd
Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding. SIAM J. Numer. Anal. 40 (5) (2002)
John P. Boyd, Andrei Natarov
Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude. Appl. Math. Comput. 126 (1) (2002)
John P. Boyd
Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm. Appl. Math. Lett. 14 (4) (2001)
John P. Boyd
The Blasius Function in the Complex Plane. Exp. Math. 8 (4) (1999)
John P. Boyd
Chebyshev and Legendre Spectral Methods in Algebraic Manipulation Languages. J. Symb. Comput. 16 (4) (1993)
John P. Boyd
An Introduction to the Numerical Analysis of Spectral Methods (Bertrand Mercier). SIAM Rev. 32 (3) (1990)
John P. Boyd
Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval. J. Sci. Comput. 3 (2) (1988)