John P. Boyd

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Three ways to solve the Poisson equation on a sphere with Gaussian forcing

Cheng Zhou, John P. Boyd, J. Boyd, 2009, J. Comput. Phys..

Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries

John P. Boyd, 2007, Comput. Math. Appl..

Four ways to compute the inverse of the complete elliptic integral of the first kind

John P. Boyd, J. Boyd, 2015, Comput. Phys. Commun..

New series for the cosine lemniscate function and the polynomialization of the lemniscate integral

John P. Boyd, 2011, J. Comput. Appl. Math..

An Introduction to the Numerical Analysis of Spectral Methods (Bertrand Mercier)

John P. Boyd, 1990, SIAM Rev..

Chapter 13: Methods for Explicit Solutions

John P. Boyd, 2014 .

Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case

John P. Boyd, Xiaolong Zhang, J. Boyd, 2020, J. Sci. Comput..

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

John P. Boyd, J. Boyd, 2017, Appl. Math. Comput..

Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods

John P. Boyd, J. Boyd, 2013, J. Comput. Appl. Math..

Hermite function interpolation on a finite uniform grid: Defeating the Runge phenomenon and replacing radial basis functions

John P. Boyd, Luis F. Alfaro, 2013, Appl. Math. Lett..

DataFlow JavaBeans for Collaborative Social Network Analysis

John P. Boyd, A. Kimball Romney, Linton C. Freeman, 2003 .

Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I

Shan Li, John P. Boyd, 2014, J. Comput. Phys..

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

Yang Xiu, John P. Boyd, 2012, Appl. Math. Comput..

Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions

John P. Boyd, Zhengjie Xu, J. Boyd, 2012, J. Comput. Phys..

Chebyshev-Fourier spectral methods in bipolar coordinates

John P. Boyd, Zhu Huang, J. Boyd, 2015, J. Comput. Phys..

Computing the real roots of a Fourier series-plus-linear-polynomial: A Chebyshev companion matrix approach

John P. Boyd, Burhan A. Sadiq, 2012, Appl. Math. Comput..

Isospectral heterogeneous domains: A numerical study

John P. Boyd, Paolo Amore, Natalia Tene Sandoval, 2019, J. Comput. Phys. X.

Large mode number eigenvalues of the prolate spheroidal differential equation

John P. Boyd, J. Boyd, 2003, Appl. Math. Comput..

The Blasius Function in the Complex Plane

John P. Boyd, J. Boyd, 1999, Exp. Math..

Divergence (Runge Phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock-Chebyshev subset interpolation

John P. Boyd, Fei Xu, 2009, Appl. Math. Comput..

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 ro

John P. Boyd, 2016, Comput. Math. Appl..

Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind

John P. Boyd, J. Boyd, 2012, Appl. Math. Comput..

Evaluating of Dawson's Integral by solving its differential equation using orthogonal rational Chebyshev functions

John P. Boyd, 2008, Appl. Math. Comput..

An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice

Lei Wang, John P. Boyd, 2009, Appl. Math. Comput..

The Fourier Transform of the quartic Gaussian exp(-Ax4): Hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to exp(-Ax2n)

John P. Boyd, J. Boyd, 2014, Appl. Math. Comput..

Solving Transcendental Equations - the Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles

John P. Boyd, J. Boyd, 2014 .

Chebyshev and Legendre Spectral Methods in Algebraic Manipulation Languages

John P. Boyd, 1993, J. Symb. Comput..

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

John P. Boyd, J. Boyd, 2005, Numerical Algorithms.

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

John P. Boyd, Zhu Huang, J. Boyd, 2019, Math. Comput. Simul..

Algorithm 840: computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions---prolate elements

John P. Boyd, J. Boyd, 2005, TOMS.

Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials

John P. Boyd, 2008, Appl. Math. Comput..

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

Lei Wang, John P. Boyd, Jianping Xiao, 2015, J. Comput. Phys..

The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems

John P. Boyd, J. Boyd, 2008, SIAM Rev..

Quartic Gaussian and Inverse-Quartic Gaussian radial basis functions: The importance of a nonnegative Fourier transform

John P. Boyd, Philip W. McCauley, J. Boyd, 2013, Comput. Math. Appl..

Rootfinding through global Newton iteration and Chebyshev polynomials for the amplitude of an electronic oscillator

John P. Boyd, Robert M. Visser, 2006, Appl. Math. Comput..

Tracing Multiple Solution Branches for Nonlinear Ordinary Differential Equations: Chebyshev and Fourier Spectral Methods and a Degree-Increasing Spectral Homotopy [DISH]

John P. Boyd, 2016, J. Sci. Comput..

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

John P. Boyd, J. Boyd, 2011, J. Comput. Phys..

High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences

John P. Boyd, Francisco M. Fernández, Paolo Amore, 2015, J. Comput. Phys..

Spectral methods in non-tensor geometry, Part II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains

Shan Li, John P. Boyd, J. Boyd, 2015, Appl. Math. Comput..

A Fourier error analysis for radial basis functions on an infinite uniform grid. Part 2: Spectral-plus is special

John P. Boyd, J. Boyd, 2013, Appl. Math. Comput..

One-point pseudospectral collocation for the one-dimensional Bratu equation

John P. Boyd, J. Boyd, 2011, Appl. Math. Comput..

Adaptive radial basis function and Hermite function pseudospectral methods for computing eigenvalues of the prolate spheroidal wave equation for very large bandwidth parameter

John P. Boyd, Zhu Huang, Jianping Xiao, 2015, J. Comput. Phys..

Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation

John P. Boyd, J. Boyd, 2003, Appl. Math. Comput..

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

John P. Boyd, J. Boyd, 2015, Appl. Math. Comput..

Approximation on non-tensor domains including squircles, Part III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids

Shan Li, John P. Boyd, J. Boyd, 2015, J. Comput. Phys..

Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: Restrictions and two improvements

John P. Boyd, Zhu Huang, J. Boyd, 2016, J. Comput. Appl. Math..

Modal preconditioning of Galerkin spectral methods: Dual bookkeeping for the Delves-Freeman iteration

John P. Boyd, Zhu Huang, J. Boyd, 2015, J. Comput. Phys..

Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n

John P. Boyd, J. Boyd, 2009, J. Comput. Phys..

Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves

John P. Boyd, 2006, Appl. Math. Comput..

Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding

John P. Boyd, 2002, SIAM J. Numer. Anal..

The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series

John P. Boyd, J. Boyd, 2010, J. Comput. Phys..

The cnoidal wave/corner wave/breaking wave scenario: A one-sided infinite-dimension bifurcation

John P. Boyd, J. Boyd, 2005, Math. Comput. Simul..

Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid

John P. Boyd, 2007, Appl. Math. Lett..

Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

John P. Boyd, Francisco M. Fernández, Paolo Amore, 2018, Comput. Phys. Commun..

Fourier embedded domain methods: extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and C∞

John P. Boyd, 2005, Appl. Math. Comput..

Accurate calculation of the solutions to the Thomas-Fermi equations

John P. Boyd, Francisco M. Fernández, Paolo Amore, 2012, Appl. Math. Comput..

Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix

John P. Boyd, J. Boyd, 2013, SIAM Rev..

All roots spectral methods: Constraints, floating point arithmetic and root exclusion

John P. Boyd, Calin-Ioan Gheorghiu, 2017, Appl. Math. Lett..

A degree-increasing [N to N+1] homotopy for Chebyshev and Fourier spectral methods

John P. Boyd, 2016, Appl. Math. Lett..

Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval

John P. Boyd, 1988, J. Sci. Comput..

Error saturation in Gaussian radial basis functions on a finite interval

John P. Boyd, J. Boyd, 2010, J. Comput. Appl. Math..

Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm

John P. Boyd, E. Campostrini, T. M. Ferraz, 2022 .

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

John P. Boyd, J. Boyd, 2007, Appl. Math. Comput..

Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude

John P. Boyd, Andrei Natarov, 2002, Appl. Math. Comput..

Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval

John P. Boyd, J. Boyd, 2010, Comput. Math. Appl..

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

Fu Yu, John P. Boyd, J. Boyd, 2011, J. Comput. Phys..

The Legendre-Burgers equation: When artificial dissipation fails

John P. Boyd, J. Boyd, 2010, Appl. Math. Comput..

The Nonconvergence of $$h$$h-Refinement in Prolate Elements

Gregor Gassner, John P. Boyd, Burhan A. Sadiq, 2013, J. Sci. Comput..

The Relationships Between Chebyshev, Legendre and Jacobi Polynomials: The Generic Superiority of Chebyshev Polynomials and Three Important Exceptions

John P. Boyd, Rolfe Petschek, 2014, J. Sci. Comput..

A comparison of companion matrix methods to find roots of a trigonometric polynomial

John P. Boyd, 2013, J. Comput. Phys..

Asymptotic coefficients for Gaussian radial basis function interpolants

Lei Wang, John P. Boyd, J. Boyd, 2010, Appl. Math. Comput..

A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences

John P. Boyd, 2006, J. Comput. Phys..

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

John P. Boyd, J. Boyd, 2006, Appl. Math. Comput..

New approximations to the principal real-valued branch of the Lambert W-function

John P. Boyd, Roberto Iacono, J. Boyd, 2017, Adv. Comput. Math..

Additive blending of local approximations into a globally-valid approximation with application to the dilogarithm

John P. Boyd, 2001, Appl. Math. Lett..

Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases pdf

John P. Boyd, Xiaolong Zhang, 2021, ArXiv.

Exact solutions to a nonlinear partial differential equation: The Product-of-Curvatures Poisson (uxxuyy=1)

John P. Boyd, Xiaolong Zhang, J. Boyd, 2021, J. Comput. Appl. Math..

The Kidder Equation: uxx+2xux/1−αu=0

John P. Boyd, Roberto Iacono, J. Boyd, 2015 .

Weakly nonlinear wavepackets in the Korteweg—de Vries equation: the KdV/NLS connection

John P. Boyd, Guan-Yu Chen, J. Boyd, 2001 .

Spectral method solution of the Stokes equations on nonstaggered grids

John P. Boyd, William W. Schultz, Mark R. Schumack, 1991 .

Two Comments on Filtering (Artificial Viscosity) for Chebyshev and Legendre Spectral and Spectral Element Methods

John P. Boyd, J. Boyd, 1998 .

Modeling nonlinear resonance: A modification to the stokes' perturbation expansion

Sue Ellen Haupt, John P. Boyd, S. Haupt, 1988 .

Solitons from sine waves: analytical and numerical methods for non-integrable solitary and cnoidal waves

John P. Boyd, J. Boyd, 1986 .

Rational chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions☆☆☆★

John P. Boyd, J. Boyd, 2001 .

Envelope Solitary Waves and Periodic Waves in the AB Equations

John P. Boyd, J. Boyd, Benkui Tan, 2002 .

New Directions in Solitons and Nonlinear Periodic Waves: Polycnoidal Waves, Imbricated Solitons, Weakly Nonlocal Solitary Waves, and Numerical Boundary Value Algorithms

John P. Boyd, J. Boyd, 1989 .

Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions

John P. Boyd, J. Boyd, 2003 .

Double cnoidal waves of the Korteweg-de Vries equation: a boundary value approach

Sue Ellen Haupt, John P. Boyd, S. E. Haupt, 1991 .

Equatorial Solitary Waves. Part 2: Envelope Solitons

John P. Boyd, 1983 .

Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboloidal travelling waves (corner and near-corner waves)

John P. Boyd, J. Boyd, 2005, European Journal of Applied Mathematics.

Spectral Modeling of Nonlinear Dispersive Waves

John P. Boyd, Nikolaos D. Katopodes, Brett F. Sanders, 1998 .

The envelope of the error for trigonometric and Chebyshev interpolation

John P. Boyd, 1990 .

A Chebyshev Polynomial Interval-Searching Method ("Lanczos Economization") for Solving a Nonlinear E

John P. Boyd, 1995 .

A lag-averaged generalization of Euler's method for accelerating series

John P. Boyd, J. Boyd, 1995 .

The nonlinear equatorial Kelvin wave

John P. Boyd, J. Boyd, 1980 .

Exponentially-Convergent Strategies for Defeating the Runge Phenomenon for the Approximation of Non-PeriodicFunctions, PartI:Single-IntervalSchemes

John P. Boyd, Jun Rong Ong, J. Boyd, 2009 .

Limited-area fourier spectral models and data analysis schemes : Windows, fourier extension, davies relaxation, and all that

John P. Boyd, J. Boyd, 2005 .

The Noninteraction of Waves with the Zonally Averaged Flow on a Spherical Earth and the Interrelationships on Eddy Fluxes of Energy, Heat and Momentum

John P. Boyd, J. Boyd, 1976 .

A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family

John P. Boyd, J. Boyd, 2003 .

Truncated Gaussian RBF Differences are Always InferiortoFiniteDifferencesof theSame StencilWidth

Lei Wang, John P. Boyd, J. Boyd, 2009 .

Equatorial Solitary Waves. Part I: Rossby Solitons

John P. Boyd, J. Boyd, 1980 .

Numerical experiments on the condition number of the interpolation matrices for radial basis functions

John P. Boyd, J. Boyd, K. Gildersleeve, 2011 .

A numerical calculation of a weakly non-local solitary wave: the φ 4 breather

John P. Boyd, 1990 .

The Choice of Spectral Functions on a Sphere for Boundary and Eigenvalue Problems: A Comparison of Chebyshev, Fourier and Associated Legendre Expansions

John P. Boyd, J. Boyd, 1978 .

A proof, based on the Euler sum acceleration, of the recovery of an exponential (geometric) rate of convergence for the Fourier series of a function with Gibbs phenomenon

John P. Boyd, 2010 .

Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves

John P. Boyd, J. Boyd, Benkui Tan, 2000 .

A Chebyshev polynomial method for computing analytic solutions to eigenvalue problems with application to the anharmonic oscillator

John P. Boyd, J. Boyd, 1978 .

Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation

John P. Boyd, Guan-Yu Chen, J. Boyd, 2001 .

The arctan/tan and Kepler-Burgers mappings for periodic solutions with a shock, front, or internal boundary layer

John P. Boyd, 1992 .

The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials

John P. Boyd, 1990 .

Weakly non-local solutions for capillary-gravity waves: fifth-degree Korteweg-de Vries equation

John P. Boyd, J. Boyd, 1991 .

Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials

John P. Boyd, Daniel H. Gally, 2007 .

Numerical study of elliptical modons using a spectral method

John P. Boyd, Hong Ma, J. Boyd, 1990, Journal of Fluid Mechanics.

Complex coordinate methods for hydrodynamic instabilities and Sturm-Liouville eigenproblems with an interior singularity

John P. Boyd, 1985 .

Long Wave/Short Wave Resonance in Equatorial Waves

John P. Boyd, J. Boyd, 1983 .

Equatorial Solitary Waves. Part 3: Westward-Traveling Modons

John P. Boyd, J. Boyd, 1985 .

Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis

John P. Boyd, J. Boyd, 2016, Am. Math. Mon..

Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding

John P. Boyd, J. Boyd, 2007 .

A Control-Volume Model of the Compressible Euler Equations with a Vertical Lagrangian Coordinate

Bram van Leer, John P. Boyd, Shian-Jiann Lin, 2013 .

Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods

John P. Boyd, Natasha Flyer, J. Boyd, 1999 .

The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series

John P. Boyd, J. Boyd, 1999 .

Rootfinding for a transcendental equation without a first guess: polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine

John P. Boyd, J. Boyd, 2007 .

Polynomial series versus sinc expansions for functions with corner or endpoint singularities

John P. Boyd, 1986 .

A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid

John P. Boyd, J. Boyd, 1992 .

Chebyshev pseudospectral method of viscous flows with corner singularities

John P. Boyd, W. W. Schultz, J. Boyd, 1989 .

Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm

John P. Boyd, J. Boyd, 1991 .

A numerical comparison of seven grids for polynomial interpolation on the interval

John P. Boyd, J. Boyd, 1999 .

Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrodinger equations

John P. Boyd, J. Boyd, Benkui Tan, 2001 .

Chebyshev Spectral Methods and the Lane-Emden Problem

John P. Boyd, J. Boyd, 2011 .

Monopolar and dipolar vortex solitons in two space dimensions

John P. Boyd, 1991 .

Exponentially-convergent strategies for defeating the Runge Phenomenon for the approximation of non-periodic functions, part two: Multi-interval polynomial schemes and multidomain Chebyshev interpolation

John P. Boyd, Jun Rong Ong, J. Boyd, 2011 .

Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions

John P. Boyd, J. Boyd, Zhen-hui Xu, 2011 .

Defeating the Runge phenomenon for equispaced polynomial interpolation via Tikhonov regularization

John P. Boyd, 1992 .

Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations

John P. Boyd, J. Boyd, 2005 .

On computation of Hough functions

John P. Boyd, J. Boyd, Houjun Wang, 2016 .

Chebyshev expansion on intervals with branch points with application to the root of Kepler's equation: A Chebyshev-Hermite-Padé method

John P. Boyd, J. Boyd, 2009 .

Asymptotic coefficients of hermite function series

John P. Boyd, J. Boyd, 1984 .