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John 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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2020 – today
- 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) - 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) - 2020
- [j76]Xiaolong Zhang
Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case. J. Sci. Comput. 82(2): 34 (2020)
2010 – 2019
- 2019
- [j75]Paolo Amore
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
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
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
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
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
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
- [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 - [j54]Paolo Amore
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
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
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
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
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
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
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
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
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
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)
2000 – 2009
- 2009
- [j30]John P. Boyd
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
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
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
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
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)
1990 – 1999
- 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)
1980 – 1989
- 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)
Coauthor Index
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