## Boyd, John Philip

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 Author ID: boyd.john-philip Published as: Boyd, John P.; Boyd, J. P.; Boyd, John Philip more...less Homepage: http://www-personal.umich.edu/~jpboyd/ External Links: MGP · ORCID · Google Scholar · ResearchGate · dblp · GND
 Documents Indexed: 199 Publications since 1978, including 4 Books 1 Further Contribution Co-Authors: 41 Co-Authors with 64 Joint Publications 557 Co-Co-Authors
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### Co-Authors

 130 single-authored 7 Tan, Benkui 5 Amore, Paolo 5 Huang, Zhu 4 Chen, Guanyu 4 Fernández, Francisco Marcelo 4 Wang, Lei 4 Zhang, Xiaolong 3 Iacono, Roberto 3 Li, Shan 3 Schultz, William W. 3 Xiao, Jianping 2 Haupt, Sue Ellen 2 Natarov, Andrei 2 Ong, Jun Rong 2 Sadiq, Burhan A. 2 Schumack, Mark R. 2 Xu, Zhengjie 2 Zhou, Cheng 1 Alfaro, Luis F. 1 Bridge, Lauren R. 1 Bucksbaum, P. H. 1 Flyer, Natasha 1 Gally, Daniel H. 1 Gassner, Gregor J. 1 Gheorghiu, Călin Ioan 1 Gildersleeve, Kenneth W. 1 Haidvogel, Dale B. 1 Iskandarani, Mohamed 1 Jacobo, Martin 1 Kowalenko, Victor 1 Ma, Hong 1 Márquez, Abigail 1 McCauley, Philip W. 1 Petschek, Rolfe 1 Rangan, Chitra 1 Rösler, Boris 1 Sousa, Alan M. 1 Visser, Robert M. 1 Wang, Houjun 1 Xiu, Yang 1 Xu, Fei 1 Yu, Fu 1 Zhevandrov, Peter N.
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### Serials

 39 Journal of Computational Physics 29 Applied Mathematics and Computation 11 Applied Numerical Mathematics 11 Journal of Scientific Computing 9 Applied Mathematics Letters 7 Journal of Mathematical Physics 7 Wave Motion 7 Journal of Computational and Applied Mathematics 6 Computers & Mathematics with Applications 6 Physica D 4 Studies in Applied Mathematics 4 SIAM Review 3 Physics Letters. A 3 Mathematics of Computation 3 Chaos, Solitons and Fractals 3 Mathematics and Computers in Simulation 2 American Mathematical Monthly 2 Computer Methods in Applied Mechanics and Engineering 2 Geophysical and Astrophysical Fluid Dynamics 2 Journal of Engineering Mathematics 2 Journal of Fluid Mechanics 2 Nonlinearity 2 Communications in Computational Physics 2 Numerical Mathematics: Theory, Methods and Applications 2 East Asian Journal on Applied Mathematics 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Physics of Fluids, A 1 Journal of Theoretical and Applied Mechanics (Sofia) 1 ACM Transactions on Mathematical Software 1 Journal of Approximation Theory 1 SIAM Journal on Numerical Analysis 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 European Journal of Applied Mathematics 1 Numerical Algorithms 1 SIAM Journal on Applied Mathematics 1 Experimental Mathematics 1 Applied and Computational Harmonic Analysis 1 Advances in Computational Mathematics 1 Vietnam Journal of Mathematics 1 The ANZIAM Journal 1 Advances in Applied Mechanics 1 Lecture Notes in Engineering 1 Mathematics and its Applications (Dordrecht) 1 Science China. Mathematics 1 Evolution Equations and Control Theory 1 Other Titles in Applied Mathematics 1 Mathematics of Climate and Weather Forecasting
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### Fields

 132 Numerical analysis (65-XX) 51 Partial differential equations (35-XX) 48 Fluid mechanics (76-XX) 39 Approximations and expansions (41-XX) 29 Ordinary differential equations (34-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 19 Special functions (33-XX) 17 Geophysics (86-XX) 6 Quantum theory (81-XX) 5 Real functions (26-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Field theory and polynomials (12-XX) 4 Functions of a complex variable (30-XX) 3 Integral equations (45-XX) 2 Sequences, series, summability (40-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Abstract harmonic analysis (43-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

173 Publications have been cited 3,255 times in 2,114 Documents Cited by Year
Chebyshev and Fourier spectral methods. 2nd rev. ed. Zbl 0994.65128
Boyd, John P.
2001
Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions. Zbl 0987.65122
Boyd, J. P.
2001
Orthogonal rational functions on a semi-infinite interval. Zbl 0614.42013
Boyd, John P.
1987
Chebyshev & Fourier spectral methods. Zbl 0681.65079
Boyd, John Philip
1989
Spectral methods using rational basis functions on an infinite interval. Zbl 0615.65090
Boyd, John P.
1987
The optimization of convergence for Chebyshev polynomial methods in an unbounded domain. Zbl 0488.65035
Boyd, John P.
1982
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds. Zbl 0999.65132
Boyd, John P.
2002
Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation. Zbl 0728.35100
Boyd, John P.
1991
Weakly nonlocal solitary waves and beyond-all-orders asymptotics. Generalized solitons and hyperasymptotic perturbation theory. Zbl 0905.76001
Boyd, John P.
1998
The devil’s invention: Asymptotic, superasymptotic and hyperasymptotic series. Zbl 0972.34044
Boyd, John P.
1999
Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms. Zbl 1059.65024
Boyd, John P.
2004
Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation. Zbl 0871.35089
Boyd, John P.
1997
Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Zbl 1025.65042
Boyd, John P.
2003
Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions. Zbl 1028.65086
Boyd, John P.; Rangan, C.; Bucksbaum, P. H.
2003
An analytical and numerical study of the two-dimensional Bratu equation. Zbl 0649.65057
Boyd, John P.
1986
Asymptotic coefficients of Hermite function series. Zbl 0551.65006
Boyd, John P.
1984
A staggered spectral element model with application to the oceanic shallow water equations. Zbl 0870.76057
Iskandarani, Mohamed; Haidvogel, Dale B.; Boyd, John P.
1995
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). Zbl 1079.35087
Boyd, John P.
2005
Chebyshev pseudospectral method of viscous flows with corner singularities. Zbl 0679.76042
Schultz, W. W.; Lee, N. Y.; Boyd, J. P.
1989
Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion. Zbl 0920.65046
Boyd, John P.
1998
Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. Zbl 1071.65189
Boyd, John P.
2005
Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. I: Single-interval schemes. Zbl 1364.65025
Boyd, John P.; Ong, Jun Rong
2009
New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly nonlocal solitary waves, and numerical boundary value algorithms. Zbl 0702.76023
Boyd, John P.
1990
Solving transcendental equations. The Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles. Zbl 1311.65047
Boyd, John P.
2014
One-point pseudospectral collocation for the one-dimensional Bratu equation. Zbl 1222.65070
Boyd, John P.
2011
Algorithm 840: Computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions – prolate elements. Zbl 1070.65569
Boyd, John P.
2005
Fourier embedded domain methods: Extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and $$C^{\infty}$$. Zbl 1061.65127
Boyd, John P.
2005
The Blasius function in the complex plane. Zbl 0980.34053
Boyd, John P.
1999
Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding. Zbl 1034.65028
Boyd, John P.
2002
Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions. Zbl 1031.65155
Boyd, John P.
2003
Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation. Zbl 1171.41004
Boyd, John P.; Xu, Fei
2009
The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems. Zbl 1152.76024
Boyd, John P.
2008
Solitons from sine waves: Analytical and numerical methods for non- integrable solitary and cnoidal waves. Zbl 0611.35080
Boyd, John P.
1986
The rate of convergence of Hermite function series. Zbl 0459.40005
Boyd, John P.
1980
Numerical experiments on the condition number of the interpolation matrices for radial basis functions. Zbl 1208.65056
Boyd, John P.; Gildersleeve, Kenneth W.
2011
Spectral method solution of the Stokes equations on nonstaggered grids. Zbl 0721.76057
Schumack, Mark R.; Schultz, William W.; Boyd, John P.
1991
Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods. Zbl 0932.65109
Boyd, John P.; Flyer, Natasha
1999
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. Zbl 1210.65192
Boyd, John P.; Yu, Fu
2011
Sturm-Liouville eigenproblems with an interior pole. Zbl 0554.34010
Boyd, John P.
1981
Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation. Zbl 0985.35077
Chen, Guanyu; Boyd, John P.
2001
A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid. Zbl 0768.65001
Boyd, John P.
1992
Rational Chebyshev series for the Thomas-Fermi function: endpoint singularities and spectral methods. Zbl 1260.65065
Boyd, John P.
2013
Complex coordinate methods for hydrodynamic instabilities and Sturm- Liouville eigenproblems with an interior singularity. Zbl 0631.76038
Boyd, John P.
1985
Chebyshev spectral methods and the Lane-Emden problem. Zbl 1249.65158
Boyd, John P.
2011
Computing real roots of a polynomial in Chebyshev series form through subdivision. Zbl 1119.65033
Boyd, John P.
2006
A numerical calculation of a weakly non-local solitary wave: The $$\phi{}^ 4$$ breather. Zbl 0743.65091
Boyd, John P.
1990
Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg-de Vries equation. Zbl 0502.35009
Boyd, John P.
1982
Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms. Zbl 1163.42001
Boyd, John P.
2009
The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials. Zbl 0717.42029
Boyd, John P.
1990
Modeling nonlinear resonance: A modification to the Stokes’ perturbation expansion. Zbl 0628.76023
Haupt, Sue Ellen; Boyd, John P.
1988
Hyperasymptotics and the linear boundary layer problem: Why asymptotic series diverge. Zbl 1087.34032
Boyd, John P.
2005
An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice. Zbl 1178.65012
Boyd, John P.; Wang, Lei
2009
Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform. Zbl 0765.65022
Boyd, John P.
1992
Asymptotic Fourier coefficients for a $$C^\infty$$ bell (smoothed-“top-hat”) & the Fourier extension problem. Zbl 1105.65129
Boyd, John P.
2006
Envelope solitary waves and periodic waves in the AB equations. Zbl 1114.76315
Tan, Benkui; Boyd, John P.
2002
Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials. Zbl 1118.65032
Boyd, John P.; Gally, Daniel H.
2007
Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width. Zbl 1364.65262
Boyd, John P.; Wang, Lei
2009
Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Zbl 1090.65052
Boyd, John P.
2006
Defeating the Runge phenomenon for equispaced polynomial interpolation via Tikhonov regularization. Zbl 0760.65007
Boyd, John P.
1992
Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals. Zbl 0666.65022
Boyd, John P.
1987
Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding. Zbl 1110.65037
Boyd, John P.
2006
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of $$1/n$$. Zbl 1159.65112
Boyd, John P.
2009
Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval. Zbl 1207.41011
Boyd, John P.
2010
The double cnoidal wave of the Korteweg-de Vries equation: An overview. Zbl 0558.35065
Boyd, John P.
1984
The asymptotic Chebyshev coefficients for functions with logarithmic endpoint singularities: Mappings and singular basis functions. Zbl 0668.65017
Boyd, John P.
1989
The rate of convergence of Fourier coefficients for entire functions of infinite order with application to the Weideman-Cloot Sinh-mapping for pseudospectral computations on an infinite interval. Zbl 0806.65146
Boyd, John P.
1994
Error saturation in Gaussian radial basis functions on a finite interval. Zbl 1189.65023
Boyd, John P.
2010
Finding the zeros of a univariate equation: Proxy rootfinders, Chebyshev interpolation, and the companion matrix. Zbl 1270.65023
Boyd, John P.
2013
Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions. Zbl 1365.76208
Boyd, John P.; Xu, Zhengjie
2011
Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation. Zbl 1163.74322
Boyd, John P.; Chen, Guan-Yu
2002
Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations. Zbl 1022.35070
Tan, Benkui; Boyd, John P.
2001
A Chebyshev polynomial interval-searching method (“Lanczos economization”) for solving a nonlinear equation with application to the nonlinear eigenvalue problem. Zbl 0823.65047
Boyd, John P.
1995
Global approximations to the principal real-valued branch of the Lambert $$W$$-function. Zbl 0940.65018
Boyd, J. P.
1998
A numerical comparison of seven grids for polynomial interpolation on the interval. Zbl 0949.65009
Boyd, J. P.
1999
Accurate calculation of the solutions to the Thomas-Fermi equations. Zbl 1410.81015
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.
2014
Weakly nonlinear wavepackets in the Korteweg-de Vries equation: The KdV/NLS connection. Zbl 0980.35146
Boyd, John P.; Chen, Guan-Yu
2001
The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation. With a foreword by John P. Boyd. Zbl 1342.41001
Kowalenko, Victor
2009
Numerical study of elliptical modons using a spectral method. Zbl 0715.76007
Boyd, John P.; Ma, Hong
1990
Polynomial series versus sinc expansions for functions with corner or endpoint singularities. Zbl 0608.65010
Boyd, John P.
1986
A lag-average generalization of Euler’s method for accelerating series. Zbl 0838.65002
Boyd, John P.
1995
Deleted residuals, the QR-factored Newton iteration, and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary, cnoidal, and shock waves. Zbl 1006.65116
Boyd, John P.
2002
The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. Zbl 1301.41003
Boyd, John P.; Petschek, Rolfe
2014
New approximations to the principal real-valued branch of the Lambert $$W$$-function. Zbl 1381.33020
Iacono, Roberto; Boyd, John P.
2017
Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the $$D_4$$ symmetry group; interpolation within a squircle. I. Zbl 1349.65056
Li, Shan; Boyd, John P.
2014
Asymptotic coefficients for Gaussian radial basis function interpolants. Zbl 1200.41001
Boyd, John P.; Wang, Lei
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. Zbl 0945.35086
Tan, Benkui; Boyd, John P.
2000
Sum-accelerated pseudospectral methods: The Euler-accelerated sinc algorithm. Zbl 0726.65019
Boyd, John P.
1991
Cnoidal waves as exact sums of repeated solitary waves: New series for elliptic functions. Zbl 0559.76019
Boyd, John P.
1984
Large mode number eigenvalues of the prolate spheroidal differential equation. Zbl 1041.34080
Boyd, John P.
2003
Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. II: Multi-interval polynomial schemes and multidomain Chebyshev interpolation. Zbl 1366.65009
Boyd, John P.; Ong, Jun Rong
2011
A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham’s equation family. Zbl 1027.65136
Boyd, John P.
2003
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. Zbl 1092.65020
Boyd, John P.
2006
Chebyshev domain truncation is inferior to Fourier domain truncation for solving problems on an infinite interval. Zbl 0666.65099
Boyd, John P.
1988
Chebyshev and Legendre spectral methods in algebraic manipulation languages. Zbl 0793.65084
Boyd, John P.
1993
The arctan/tan and Kepler-Burgers mappings for periodic solutions with a shock, front, or internal boundary layer. Zbl 0760.65106
Boyd, John P.
1992
High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. Zbl 1352.65458
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris
2016
Sum-accelerated pseudospectral methods: Finite differences and sech-weighted differences. Zbl 0845.65041
Boyd, John P.
1994
Construction of Lighthill’s unitary functions: The imbricate series of unity. Zbl 0909.42004
Boyd, John P.
1997
Near-corner waves of the Camassa-Holm equation. Zbl 1136.35445
Boyd, John P.
2005
Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation. Zbl 1136.74330
Boyd, John P.
2005
Optimal truncations for multivariate Fourier and Chebyshev series: mysteries of the hyperbolic cross. I: bivariate case. Zbl 1465.42004
Zhang, Xiaolong; Boyd, John P.
2020
Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations. Zbl 06969471
Zhang, Xiaolong; Boyd, John P.
2019
High order analysis of the limit cycle of the van der Pol oscillator. Zbl 1383.34076
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.
2018
New approximations to the principal real-valued branch of the Lambert $$W$$-function. Zbl 1381.33020
Iacono, Roberto; Boyd, John P.
2017
All roots spectral methods: constraints, floating point arithmetic and root exclusion. Zbl 1358.65049
Boyd, John P.; Gheorghiu, Călin-Ioan
2017
The Crane equation $$u u_{x x} = - 2$$: the general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities. Zbl 1411.76112
Boyd, John P.
2017
High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. Zbl 1352.65458
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris
2016
A degree-increasing [$$N$$ to $$N+1$$] homotopy for Chebyshev and Fourier spectral methods. Zbl 1334.65122
Boyd, John P.
2016
Tracing multiple solution branches for nonlinear ordinary differential equations: Chebyshev and Fourier spectral methods and a degree-increasing spectral homotopy [DISH]. Zbl 1371.65070
Boyd, John P.
2016
Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: restrictions and two improvements. Zbl 1416.65478
Huang, Zhu; Boyd, John P.
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. Zbl 1443.65104
Boyd, John P.
2016
RBF-vortex methods for the barotropic vorticity equation on a sphere. Zbl 1351.86009
Xiao, Jianping; Wang, Lei; Boyd, John P.
2015
Simple analytic approximations for the Blasius problem. Zbl 1364.76040
Iacono, R.; Boyd, John P.
2015
Adaptive radial basis function and Hermite function pseudospectral methods for computing eigenvalues of the prolate spheroidal wave equation for very large bandwidth parameter. Zbl 1352.65566
Huang, Zhu; Xiao, Jianping; Boyd, John P.
2015
Approximation on non-tensor domains including squircles. III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids. Zbl 1352.65036
Li, Shan; Boyd, John P.
2015
The Kidder equation: $$u_{xx}+2xu_x/\sqrt{1-\alpha u}=0$$. Zbl 1327.65142
Iacono, Roberto; Boyd, John P.
2015
Four ways to compute the inverse of the complete elliptic integral of the first kind. Zbl 1360.65080
Boyd, John P.
2015
A Fourier error analysis for radial basis functions and the discrete singular convolution on an infinite uniform grid. I: Error theorem and diffusion in Fourier space. Zbl 1410.65015
Boyd, John P.
2015
Spectral methods in non-tensor geometry. II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains. Zbl 1410.65022
Li, Shan; Boyd, John P.
2015
Solving transcendental equations. The Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles. Zbl 1311.65047
Boyd, John P.
2014
Accurate calculation of the solutions to the Thomas-Fermi equations. Zbl 1410.81015
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.
2014
The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. Zbl 1301.41003
Boyd, John P.; Petschek, Rolfe
2014
Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the $$D_4$$ symmetry group; interpolation within a squircle. I. Zbl 1349.65056
Li, Shan; Boyd, John P.
2014
The Fourier transform of the quartic Gaussian $$\exp(-Ax^4)$$: hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to $$\exp(-Ax^{2 n})$$. Zbl 1334.42011
Boyd, John P.
2014
Rational Chebyshev series for the Thomas-Fermi function: endpoint singularities and spectral methods. Zbl 1260.65065
Boyd, John P.
2013
Finding the zeros of a univariate equation: Proxy rootfinders, Chebyshev interpolation, and the companion matrix. Zbl 1270.65023
Boyd, John P.
2013
The nonconvergence of $$h$$-refinement in prolate elements. Zbl 1282.65148
Boyd, John P.; Gassner, Gregor; Sadiq, Burhan A.
2013
Hermite function interpolation on a finite uniform grid: defeating the Runge phenomenon and replacing radial basis functions. Zbl 1308.65019
Boyd, John P.; Alfaro, Luis F.
2013
Quartic Gaussian and inverse-quartic Gaussian radial basis functions: the importance of a nonnegative Fourier transform. Zbl 1268.41014
Boyd, John P.; McCauley, Philip W.
2013
A comparison of companion matrix methods to find roots of a trigonometric polynomial. Zbl 1349.65156
Boyd, John P.
2013
A Fourier error analysis for radial basis functions on an infinite uniform grid. II: Spectral-plus is special. Zbl 1334.65036
Boyd, John P.
2013
Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions. Zbl 1408.65070
Boyd, John P.; Xu, Zhengjie
2012
Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind. Zbl 1243.65035
Boyd, John P.
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. Zbl 1311.42007
Boyd, John P.; Xiu, Yang (Chris)
2012
One-point pseudospectral collocation for the one-dimensional Bratu equation. Zbl 1222.65070
Boyd, John P.
2011
Numerical experiments on the condition number of the interpolation matrices for radial basis functions. Zbl 1208.65056
Boyd, John P.; Gildersleeve, Kenneth W.
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. Zbl 1210.65192
Boyd, John P.; Yu, Fu
2011
Chebyshev spectral methods and the Lane-Emden problem. Zbl 1249.65158
Boyd, John P.
2011
Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions. Zbl 1365.76208
Boyd, John P.; Xu, Zhengjie
2011
Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. II: Multi-interval polynomial schemes and multidomain Chebyshev interpolation. Zbl 1366.65009
Boyd, John P.; Ong, Jun Rong
2011
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. Zbl 1217.65037
Boyd, John P.
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. Zbl 1210.65029
Boyd, John P.
2011
New series for the cosine lemniscate function and the polynomialization of the lemniscate integral. Zbl 1209.65028
Boyd, John P.
2011
Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval. Zbl 1207.41011
Boyd, John P.
2010
Error saturation in Gaussian radial basis functions on a finite interval. Zbl 1189.65023
Boyd, John P.
2010
Asymptotic coefficients for Gaussian radial basis function interpolants. Zbl 1200.41001
Boyd, John P.; Wang, Lei
2010
Sensitivity of RBF interpolation on an otherwise uniform grid with a point omitted or slightly shifted. Zbl 1193.65014
Boyd, John P.; Bridge, Lauren R.
2010
The uselessness of the fast Gauss transform for summing Gaussian radial basis function series. Zbl 1180.65185
Boyd, John P.
2010
The Legendre-Burgers equation: when artificial dissipation fails. Zbl 1342.76094
Boyd, John P.
2010
Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. I: Single-interval schemes. Zbl 1364.65025
Boyd, John P.; Ong, Jun Rong
2009
Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation. Zbl 1171.41004
Boyd, John P.; Xu, Fei
2009
Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms. Zbl 1163.42001
Boyd, John P.
2009
An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice. Zbl 1178.65012
Boyd, John P.; Wang, Lei
2009
Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width. Zbl 1364.65262
Boyd, John P.; Wang, Lei
2009
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of $$1/n$$. Zbl 1159.65112
Boyd, John P.
2009
The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation. With a foreword by John P. Boyd. Zbl 1342.41001
Kowalenko, Victor
2009
Chebyshev expansion on intervals with branch points with application to the root of Kepler’s equation: A Chebyshev-Hermite-Padé method. Zbl 1152.65024
Boyd, John P.
2009
Three ways to solve the Poisson equation on a sphere with Gaussian forcing. Zbl 1173.65068
Boyd, John P.; Zhou, Cheng
2009
An SVD analysis of equispaced polynomial interpolation. Zbl 1175.65020
Boyd, John P.; Sousa, Alan M.
2009
The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems. Zbl 1152.76024
Boyd, John P.
2008
Evaluating of Dawson’s integral by solving its differential equation using orthogonal rational Chebyshev functions. Zbl 1157.65331
Boyd, John P.
2008
Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials. Zbl 1138.65024
Boyd, John P.
2008
Kelvin waves in the nonlinear shallow water equations on the sphere: nonlinear travelling waves and the corner wave bifurcation. Zbl 1155.76013
Boyd, John P.; Zhou, Cheng
2008
Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials. Zbl 1118.65032
Boyd, John P.; Gally, Daniel H.
2007
Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid. Zbl 1152.65404
Boyd, John P.
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. Zbl 1121.65049
Boyd, John P.
2007
Rootfinding for a transcendental equation without a first guess: polynomialization of Kepler’s equation through Chebyshev polynomial expansion of the sine. Zbl 1105.65054
Boyd, John P.
2007
Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries. Zbl 1132.65039
Boyd, John P.
2007
Planetary solitary waves. Zbl 1316.76023
Boyd, J. P.
2007
Computing real roots of a polynomial in Chebyshev series form through subdivision. Zbl 1119.65033
Boyd, John P.
2006
Asymptotic Fourier coefficients for a $$C^\infty$$ bell (smoothed-“top-hat”) & the Fourier extension problem. Zbl 1105.65129
Boyd, John P.
2006
Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Zbl 1090.65052
Boyd, John P.
2006
Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding. Zbl 1110.65037
Boyd, John P.
2006
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. Zbl 1092.65020
Boyd, John P.
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. Zbl 1331.76082
Boyd, John P.
2006
Rootfinding through global Newton iteration and Chebyshev polynomials for the amplitude of an electronic oscillator. Zbl 1106.65113
Boyd, John P.; Visser, Robert M.
2006
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). Zbl 1079.35087
Boyd, John P.
2005
Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. Zbl 1071.65189
Boyd, John P.
2005
Algorithm 840: Computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions – prolate elements. Zbl 1070.65569
Boyd, John P.
2005
Fourier embedded domain methods: Extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and $$C^{\infty}$$. Zbl 1061.65127
Boyd, John P.
2005
Hyperasymptotics and the linear boundary layer problem: Why asymptotic series diverge. Zbl 1087.34032
Boyd, John P.
2005
Near-corner waves of the Camassa-Holm equation. Zbl 1136.35445
Boyd, John P.
2005
Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation. Zbl 1136.74330
Boyd, John P.
2005
The cnoidal wave/corner wave/breaking wave scenario: a one-sided infinite-dimension bifurcation. Zbl 1070.35027
Boyd, John P.
2005
A Chebyshev/rational Chebyshev spectral method for the Helmholtz equation in a sector on the surface of a sphere: defeating corner singularities. Zbl 1072.65153
Boyd, John P.
2005
Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms. Zbl 1059.65024
Boyd, John P.
2004
Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Zbl 1025.65042
Boyd, John P.
2003
Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: A comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions. Zbl 1028.65086
Boyd, John P.; Rangan, C.; Bucksbaum, P. H.
2003
Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions. Zbl 1031.65155
Boyd, John P.
2003
Large mode number eigenvalues of the prolate spheroidal differential equation. Zbl 1041.34080
Boyd, John P.
2003
A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham’s equation family. Zbl 1027.65136
Boyd, John P.
2003
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds. Zbl 0999.65132
Boyd, John P.
2002
Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding. Zbl 1034.65028
Boyd, John P.
2002
Envelope solitary waves and periodic waves in the AB equations. Zbl 1114.76315
Tan, Benkui; Boyd, John P.
2002
Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation. Zbl 1163.74322
Boyd, John P.; Chen, Guan-Yu
2002
Deleted residuals, the QR-factored Newton iteration, and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary, cnoidal, and shock waves. Zbl 1006.65116
Boyd, John P.
2002
Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude. Zbl 1215.76017
Boyd, John P.; Natarov, Andrei
2002
Nonlinear wave packets of equatorial Kelvin waves. Zbl 1206.76009
Chen, Guan-Yu; Boyd, John P.
2002
Chebyshev and Fourier spectral methods. 2nd rev. ed. Zbl 0994.65128
Boyd, John P.
2001
Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions. Zbl 0987.65122
Boyd, J. P.
2001
...and 73 more Documents
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### Cited by 3,014 Authors

 128 Boyd, John Philip 28 Wang, Zhongqing 27 Doha, Eid H. 27 Guo, Ben-Yu 23 Dehghan Takht Fooladi, Mehdi 22 Wang, Lilian 18 Abd-Elhameed, Waleed Mohamed 18 Parand, Kourosh 17 Shen, Jie 16 Bhrawy, Ali Hassan 16 Li, Huiyuan 15 Wang, Cheng 15 Wang, Tianjun 14 Giraldo, Francis X. 14 Karoui, Abderrazek 14 Youssri, Youssri H. 13 Adcock, Ben 13 Grimshaw, Roger Hamilton James 13 Lustri, Christopher J. 12 Bruno, Oscar P. 12 Huybrechs, Daan 11 Hafez, Ramy Mahmoud 11 Townsend, Alex 10 Hesthaven, Jan S. 9 Delkhosh, Mehdi 9 Karageorghis, Andreas 9 Liu, Zhengrong 9 Nicholls, David P. 9 Trefethen, Lloyd Nicholas 9 Wazwaz, Abdul-Majid Abdul-Rahman 9 Yun, Beong In 9 Zhang, Zhimin 8 Coclite, Giuseppe Maria 8 Julien, Keith A. 8 Livermore, Philip W. 8 Zhang, Chao 7 Akylas, T. R. 7 Amore, Paolo 7 Champneys, Alan R. 7 Cheng, Kelong 7 de la Hoz, Francisco 7 de Oliveira, H. P. 7 Di Ruvo, Lorenzo 7 Diamessis, Peter J. 7 Fakhar-Izadi, Farhad 7 Heydari, Mohammad Hossien 7 Hogan, Jeffrey A. 7 Lakey, Joseph D. 7 Li, Shan 7 Olver, Sheehan Shakiban 7 Pelinovsky, Dmitry Efimovich 7 Sun, Tao 7 Wang, Xinwei 7 Wise, Steven M. 6 Abbasbandy, Saeid 6 Cui, Shangbin 6 Deville, Michel O. 6 Gelb, Anne 6 Gheorghiu, Călin Ioan 6 Iskandarani, Mohamed 6 Jung, Jae-Hun 6 Kiliçman, Adem 6 Leriche, Emmanuel 6 Maleki, Mohammad Reza 6 Morais, João Pedro 6 Nakatsukasa, Yuji 6 Protas, Bartosz 6 Shizgal, Bernie D. 6 Vianello, Marco 6 Xiang, Shuhuang 6 Yang, Haizhao 6 Yang, Jianke 6 Yi, Lijun 6 Yu, Xuhong 6 Zhang, Jing 5 Akers, Benjamin F. 5 Alharbi, Fahhad H. 5 Bonami, Aline 5 Chapman, Stephen Jonathan 5 Daripa, Prabir K. 5 Fernández, Francisco Marcelo 5 Fischer, Paul F. 5 Flyer, Natasha 5 Geng, Xianguo 5 Jia, Hongli 5 Johnson, Edward Robert 5 Kazem, Saeed 5 Kizner, Ziv 5 Malomed, Boris A. 5 McClarren, Ryan G. 5 Pasquetti, Richard 5 Qiu, Jingmei 5 Sommariva, Alvise 5 Tang, Tao 5 Trinh, Philippe H. 5 Vasil, Geoffrey M. 5 Xiong, Tao 5 Xu, Chuanju 4 Asgari, Zohreh 4 Auteri, Franco ...and 2,914 more Authors
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### Cited in 340 Serials

 258 Journal of Computational Physics 93 Applied Mathematics and Computation 89 Journal of Scientific Computing 82 Journal of Computational and Applied Mathematics 71 Journal of Fluid Mechanics 61 Applied Numerical Mathematics 47 Physica D 44 SIAM Journal on Scientific Computing 38 Mathematics of Computation 37 Computers & Mathematics with Applications 36 Numerical Algorithms 32 Communications in Nonlinear Science and Numerical Simulation 30 Computers and Fluids 27 Engineering Analysis with Boundary Elements 25 Computer Physics Communications 25 Mathematics and Computers in Simulation 24 Wave Motion 24 Physics of Fluids 23 Journal of High Energy Physics 22 Computer Methods in Applied Mechanics and Engineering 22 Applied Mathematics Letters 21 Chaos, Solitons and Fractals 20 International Journal of Computer Mathematics 18 International Journal for Numerical Methods in Fluids 18 Mathematical Methods in the Applied Sciences 18 Numerical Methods for Partial Differential Equations 17 Journal of Mathematical Physics 17 Advances in Computational Mathematics 16 Computational and Applied Mathematics 15 Abstract and Applied Analysis 14 Journal of Mathematical Analysis and Applications 14 Applied Mathematical Modelling 14 Applied and Computational Harmonic Analysis 14 Nonlinear Dynamics 14 European Journal of Mechanics. B. Fluids 13 Journal of Engineering Mathematics 13 SIAM Journal on Numerical Analysis 13 International Journal of Applied and Computational Mathematics 12 BIT 12 Studies in Applied Mathematics 11 The Journal of Fourier Analysis and Applications 11 Mathematical Problems in Engineering 10 Acta Mechanica 10 East Asian Journal on Applied Mathematics 9 Classical and Quantum Gravity 9 International Journal for Numerical Methods in Engineering 9 Journal of Differential Equations 9 Numerische Mathematik 9 Journal of Applied Mathematics 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Chaos 7 General Relativity and Gravitation 7 Physics Letters. A 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Theoretical and Computational Fluid Dynamics 7 Mathematical and Computer Modelling 7 Journal of Mathematical Chemistry 7 Advances in Difference Equations 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Computational Mathematics and Mathematical Physics 6 Foundations of Computational Mathematics 6 S$$\vec{\text{e}}$$MA Journal 6 Computational Methods for Differential Equations 5 Geophysical and Astrophysical Fluid Dynamics 5 Mathematical Notes 5 Transport Theory and Statistical Physics 5 Journal of Approximation Theory 5 Quarterly of Applied Mathematics 5 Constructive Approximation 5 Journal of the Egyptian Mathematical Society 5 Acta Mathematica Sinica. English Series 5 Nonlinear Analysis. Real World Applications 4 American Mathematical Monthly 4 Applicable Analysis 4 Communications in Mathematical Physics 4 Fluid Dynamics 4 International Journal of Heat and Mass Transfer 4 Physics of Fluids, A 4 Calcolo 4 Computational Mechanics 4 SIAM Journal on Matrix Analysis and Applications 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Annals of Physics 4 SIAM Journal on Applied Mathematics 4 SIAM Review 4 Journal of Nonlinear Science 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 The ANZIAM Journal 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 SIAM Journal on Applied Dynamical Systems 4 Multiscale Modeling & Simulation 4 Journal of Cosmology and Astroparticle Physics 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Communications in Computational Physics 4 Advances in Applied Mathematics and Mechanics 4 SIAM/ASA Journal on Uncertainty Quantification 4 Communications on Applied Mathematics and Computation 3 International Journal of Control 3 International Journal of Engineering Science ...and 240 more Serials
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### Cited in 52 Fields

 1,206 Numerical analysis (65-XX) 692 Partial differential equations (35-XX) 553 Fluid mechanics (76-XX) 229 Ordinary differential equations (34-XX) 181 Approximations and expansions (41-XX) 160 Harmonic analysis on Euclidean spaces (42-XX) 140 Special functions (33-XX) 111 Dynamical systems and ergodic theory (37-XX) 101 Mechanics of deformable solids (74-XX) 84 Geophysics (86-XX) 73 Quantum theory (81-XX) 62 Statistical mechanics, structure of matter (82-XX) 56 Integral equations (45-XX) 54 Relativity and gravitational theory (83-XX) 51 Optics, electromagnetic theory (78-XX) 44 Biology and other natural sciences (92-XX) 33 Classical thermodynamics, heat transfer (80-XX) 31 Systems theory; control (93-XX) 27 Probability theory and stochastic processes (60-XX) 27 Computer science (68-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 25 Real functions (26-XX) 25 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Information and communication theory, circuits (94-XX) 24 Astronomy and astrophysics (85-XX) 23 Operator theory (47-XX) 22 Mechanics of particles and systems (70-XX) 21 Functions of a complex variable (30-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 17 Statistics (62-XX) 15 Operations research, mathematical programming (90-XX) 12 Functional analysis (46-XX) 11 Number theory (11-XX) 10 Difference and functional equations (39-XX) 9 Integral transforms, operational calculus (44-XX) 8 Sequences, series, summability (40-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Field theory and polynomials (12-XX) 5 Combinatorics (05-XX) 5 Potential theory (31-XX) 5 Differential geometry (53-XX) 4 Commutative algebra (13-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX)