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ORCIDJohn P. Boyd 0001
John Philip Boyd
Person information
- affiliation: University of Michigan, Department of Atmospheric, Oceanic & Space Science, Ann Arbor, MI, USA
Other persons with the same name
- John P. Boyd 0002 (aka: John Paul Boyd) — University of California, Irvine, CA, USA
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Books and Theses
- 2014
[b1]John P. Boyd:
Solving Transcendental Equations - the Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles. SIAM 2014, ISBN 978-1-611-97351-8, pp. I-XVIII, 1-460
Journal Articles
- 2023
- [j78]John P. Boyd:
Using parity to accelerate Hermite function computations: Zeros of truncated Hermite series, Gaussian quadrature and Clenshaw summation. Math. Comput. Simul. 207: 521-532 (2023) - 2022
- [j77]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: 113866 (2022) - 2020
- [j76]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): 34 (2020) - 2019
- [j75]Paolo Amore, John P. Boyd, Natalia Tene Sandoval:
Isospectral heterogeneous domains: A numerical study. J. Comput. Phys. X 1: 100018 (2019) - [j74]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: 82-102 (2019) - 2018
- [j73]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: 209-221 (2018) - 2017
- [j72]Roberto Iacono, John P. Boyd:
New approximations to the principal real-valued branch of the Lambert W-function. Adv. Comput. Math. 43(6): 1403-1436 (2017) - [j71]John P. Boyd:
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. 301: 214-223 (2017) - [j70]John P. Boyd, Calin-Ioan Gheorghiu:
All roots spectral methods: Constraints, floating point arithmetic and root exclusion. Appl. Math. Lett. 67: 28-32 (2017) - [j69]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): 306-323 (2017) - 2016
- [j68]John P. Boyd:
A degree-increasing [N to N+1] homotopy for Chebyshev and Fourier spectral methods. Appl. Math. Lett. 57: 77-81 (2016) - [j67]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): 1227-1241 (2016) - [j66]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: 340-355 (2016) - [j65]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: 252-271 (2016) - [j64]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): 1115-1143 (2016) - [j63]John P. Boyd:
Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis. Am. Math. Mon. 123(3): 241-257 (2016) - 2015
- [j62]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: 132-140 (2015) - [j61]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: 759-774 (2015) - [j60]John P. Boyd:
Four ways to compute the inverse of the complete elliptic integral of the first kind. Comput. Phys. Commun. 196: 13-18 (2015) - [j59]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: 269-284 (2015) - [j58]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: 653-668 (2015) - [j57]Jianping Xiao, Lei Wang, John P. Boyd:
RBF-vortex methods for the barotropic vorticity equation on a sphere. J. Comput. Phys. 285: 208-225 (2015) - [j56]Zhu Huang, John P. Boyd:
Chebyshev-Fourier spectral methods in bipolar coordinates. J. Comput. Phys. 295: 46-64 (2015) - [j55]Zhu Huang, John P. Boyd:
Modal preconditioning of Galerkin spectral methods: Dual bookkeeping for the Delves-Freeman iteration. J. Comput. Phys. 300: 1-4 (2015) - 2014
- [j54]Paolo Amore, John P. Boyd, Francisco M. Fernández:
Accurate calculation of the solutions to the Thomas-Fermi equations. Appl. Math. Comput. 232: 929-943 (2014) - [j53]John P. Boyd:
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. 241: 75-87 (2014) - [j52]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: 931-947 (2014) - [j51]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): 1-27 (2014) - 2013
- [j50]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: 695-707 (2013) - [j49]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): 995-997 (2013) - [j48]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): 75-88 (2013) - [j47]John P. Boyd:
Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods. J. Comput. Appl. Math. 244: 90-101 (2013) - [j46]John P. Boyd:
A comparison of companion matrix methods to find roots of a trigonometric polynomial. J. Comput. Phys. 246: 96-112 (2013) - [j45]John P. Boyd, Gregor Gassner, Burhan A. Sadiq:
The Nonconvergence of $$h$$ h -Refinement in Prolate Elements. J. Sci. Comput. 57(2): 372-389 (2013) - [j44]John P. Boyd:
Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix. SIAM Rev. 55(2): 375-396 (2013) - 2012
- [j43]John P. Boyd:
Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind. Appl. Math. Comput. 218(13): 7005-7013 (2012) - [j42]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): 819-826 (2012) - [j41]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): 3461-3468 (2012) - [j40]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): 1216-1229 (2012) - 2011
- [j39]John P. Boyd:
One-point pseudospectral collocation for the one-dimensional Bratu equation. Appl. Math. Comput. 217(12): 5553-5565 (2011) - [j38]John P. Boyd:
New series for the cosine lemniscate function and the polynomialization of the lemniscate integral. J. Comput. Appl. Math. 235(8): 1941-1955 (2011) - [j37]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): 1304-1318 (2011) - [j36]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): 1408-1438 (2011) - 2010
- [j35]John P. Boyd, Lei Wang:
Asymptotic coefficients for Gaussian radial basis function interpolants. Appl. Math. Comput. 216(8): 2394-2407 (2010) - [j34]John P. Boyd:
The Legendre-Burgers equation: When artificial dissipation fails. Appl. Math. Comput. 217(5): 1949-1964 (2010) - [j33]John P. Boyd:
Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval. Comput. Math. Appl. 60(12): 3108-3122 (2010) - [j32]John P. Boyd:
Error saturation in Gaussian radial basis functions on a finite interval. J. Comput. Appl. Math. 234(5): 1435-1441 (2010) - [j31]John P. Boyd:
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series. J. Comput. Phys. 229(4): 1311-1326 (2010) - 2009
- [j30]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): 158-168 (2009) - [j29]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): 2215-2223 (2009) - [j28]John P. Boyd:
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n. J. Comput. Phys. 228(5): 1404-1411 (2009) - [j27]John P. Boyd, Cheng Zhou:
Three ways to solve the Poisson equation on a sphere with Gaussian forcing. J. Comput. Phys. 228(13): 4702-4713 (2009) - 2008
- [j26]John P. Boyd:
Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials. Appl. Math. Comput. 198(2): 925-929 (2008) - [j25]John P. Boyd:
Evaluating of Dawson's Integral by solving its differential equation using orthogonal rational Chebyshev functions. Appl. Math. Comput. 204(2): 914-919 (2008) - [j24]John P. Boyd:
The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems. SIAM Rev. 50(4): 791-804 (2008) - 2007
- [j23]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): 1780-1789 (2007) - [j22]John P. Boyd:
Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid. Appl. Math. Lett. 20(9): 971-975 (2007) - [j21]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): 336-349 (2007) - [j20]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): 72-81 (2007) - 2006
- [j19]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): 1642-1658 (2006) - [j18]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): 289-299 (2006) - [j17]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): 166-174 (2006) - [j16]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): 538-549 (2006) - [j15]John P. Boyd:
Asymptotic Fourier Coefficients for a C infinity Bell (Smoothed-"Top-Hat") & the Fourier Extension Problem. J. Sci. Comput. 29(1): 1-24 (2006) - 2005
- [j14]John P. Boyd:
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. 161(2): 591-597 (2005) - [j13]John P. Boyd:
The cnoidal wave/corner wave/breaking wave scenario: A one-sided infinite-dimension bifurcation. Math. Comput. Simul. 69(3-4): 235-242 (2005) - [j12]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): 197-207 (2005) - [j11]John P. Boyd:
Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge. SIAM Rev. 47(3): 553-575 (2005) - [j10]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): 149-165 (2005) - 2003
- [j9]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): 189-200 (2003) - [j8]John P. Boyd:
Large mode number eigenvalues of the prolate spheroidal differential equation. Appl. Math. Comput. 145(2-3): 881-886 (2003) - 2002
- [j7]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): 109-117 (2002) - [j6]John P. Boyd:
Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding. SIAM J. Numer. Anal. 40(5): 1666-1682 (2002) - 2001
- [j5]John P. Boyd:
Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm. Appl. Math. Lett. 14(4): 477-481 (2001) - 1999
- [j4]John P. Boyd:
The Blasius Function in the Complex Plane. Exp. Math. 8(4): 381-394 (1999) - 1993
- [j3]John P. Boyd:
Chebyshev and Legendre Spectral Methods in Algebraic Manipulation Languages. J. Symb. Comput. 16(4): 377-399 (1993) - 1990
- [j2]John P. Boyd:
An Introduction to the Numerical Analysis of Spectral Methods (Bertrand Mercier). SIAM Rev. 32(3): 489-490 (1990) - 1988
- [j1]John P. Boyd:
Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval. J. Sci. Comput. 3(2): 109-120 (1988)
Informal and Other Publications
- 2021
- [i1]Xiaolong Zhang, John P. Boyd:
Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases. CoRR abs/2103.11841 (2021)
Coauthor Index
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