Edit Profile (opens in new tab) Boyd, John Philip Compute Distance To: Compute 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 all top 5 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. all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0994.65128Boyd, John P. 676 2001 Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions. Zbl 0987.65122Boyd, J. P. 213 2001 Orthogonal rational functions on a semi-infinite interval. Zbl 0614.42013Boyd, John P. 94 1987 Chebyshev & Fourier spectral methods. Zbl 0681.65079Boyd, John Philip 92 1989 Spectral methods using rational basis functions on an infinite interval. Zbl 0615.65090Boyd, John P. 90 1987 The optimization of convergence for Chebyshev polynomial methods in an unbounded domain. Zbl 0488.65035Boyd, John P. 67 1982 A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds. Zbl 0999.65132Boyd, John P. 64 2002 Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation. Zbl 0728.35100Boyd, John P. 63 1991 Weakly nonlocal solitary waves and beyond-all-orders asymptotics. Generalized solitons and hyperasymptotic perturbation theory. Zbl 0905.76001Boyd, John P. 60 1998 The devil’s invention: Asymptotic, superasymptotic and hyperasymptotic series. Zbl 0972.34044Boyd, John P. 57 1999 Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms. Zbl 1059.65024Boyd, John P. 50 2004 Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation. Zbl 0871.35089Boyd, John P. 48 1997 Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Zbl 1025.65042Boyd, John P. 47 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 1028.65086Boyd, John P.; Rangan, C.; Bucksbaum, P. H. 40 2003 An analytical and numerical study of the two-dimensional Bratu equation. Zbl 0649.65057Boyd, John P. 38 1986 Asymptotic coefficients of Hermite function series. Zbl 0551.65006Boyd, John P. 36 1984 A staggered spectral element model with application to the oceanic shallow water equations. Zbl 0870.76057Iskandarani, Mohamed; Haidvogel, Dale B.; Boyd, John P. 35 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 1079.35087Boyd, John P. 35 2005 Chebyshev pseudospectral method of viscous flows with corner singularities. Zbl 0679.76042Schultz, W. W.; Lee, N. Y.; Boyd, J. P. 33 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 0920.65046Boyd, John P. 33 1998 Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. Zbl 1071.65189Boyd, John P. 32 2005 Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. I: Single-interval schemes. Zbl 1364.65025Boyd, John P.; Ong, Jun Rong 31 2009 New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly nonlocal solitary waves, and numerical boundary value algorithms. Zbl 0702.76023Boyd, John P. 29 1990 Solving transcendental equations. The Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles. Zbl 1311.65047Boyd, John P. 29 2014 One-point pseudospectral collocation for the one-dimensional Bratu equation. Zbl 1222.65070Boyd, John P. 29 2011 Algorithm 840: Computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions – prolate elements. Zbl 1070.65569Boyd, John P. 28 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 1061.65127Boyd, John P. 28 2005 The Blasius function in the complex plane. Zbl 0980.34053Boyd, John P. 28 1999 Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding. Zbl 1034.65028Boyd, John P. 28 2002 Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions. Zbl 1031.65155Boyd, John P. 28 2003 Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation. Zbl 1171.41004Boyd, John P.; Xu, Fei 28 2009 The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems. Zbl 1152.76024Boyd, John P. 25 2008 Solitons from sine waves: Analytical and numerical methods for non- integrable solitary and cnoidal waves. Zbl 0611.35080Boyd, John P. 24 1986 The rate of convergence of Hermite function series. Zbl 0459.40005Boyd, John P. 24 1980 Numerical experiments on the condition number of the interpolation matrices for radial basis functions. Zbl 1208.65056Boyd, John P.; Gildersleeve, Kenneth W. 24 2011 Spectral method solution of the Stokes equations on nonstaggered grids. Zbl 0721.76057Schumack, Mark R.; Schultz, William W.; Boyd, John P. 23 1991 Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods. Zbl 0932.65109Boyd, John P.; Flyer, Natasha 23 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 1210.65192Boyd, John P.; Yu, Fu 23 2011 Sturm-Liouville eigenproblems with an interior pole. Zbl 0554.34010Boyd, John P. 19 1981 Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation. Zbl 0985.35077Chen, Guanyu; Boyd, John P. 19 2001 A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid. Zbl 0768.65001Boyd, John P. 18 1992 Rational Chebyshev series for the Thomas-Fermi function: endpoint singularities and spectral methods. Zbl 1260.65065Boyd, John P. 18 2013 Complex coordinate methods for hydrodynamic instabilities and Sturm- Liouville eigenproblems with an interior singularity. Zbl 0631.76038Boyd, John P. 17 1985 Chebyshev spectral methods and the Lane-Emden problem. Zbl 1249.65158Boyd, John P. 17 2011 Computing real roots of a polynomial in Chebyshev series form through subdivision. Zbl 1119.65033Boyd, John P. 17 2006 A numerical calculation of a weakly non-local solitary wave: The \(\phi{}^ 4\) breather. Zbl 0743.65091Boyd, John P. 16 1990 Theta functions, Gaussian series, and spatially periodic solutions of the Korteweg-de Vries equation. Zbl 0502.35009Boyd, John P. 16 1982 Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms. Zbl 1163.42001Boyd, John P. 15 2009 The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials. Zbl 0717.42029Boyd, John P. 14 1990 Modeling nonlinear resonance: A modification to the Stokes’ perturbation expansion. Zbl 0628.76023Haupt, Sue Ellen; Boyd, John P. 14 1988 Hyperasymptotics and the linear boundary layer problem: Why asymptotic series diverge. Zbl 1087.34032Boyd, John P. 14 2005 An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice. Zbl 1178.65012Boyd, John P.; Wang, Lei 14 2009 Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast Fourier transform. Zbl 0765.65022Boyd, John P. 13 1992 Asymptotic Fourier coefficients for a \(C^\infty\) bell (smoothed-“top-hat”) & the Fourier extension problem. Zbl 1105.65129Boyd, John P. 13 2006 Envelope solitary waves and periodic waves in the AB equations. Zbl 1114.76315Tan, Benkui; Boyd, John P. 13 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 1118.65032Boyd, John P.; Gally, Daniel H. 13 2007 Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width. Zbl 1364.65262Boyd, John P.; Wang, Lei 13 2009 Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Zbl 1090.65052Boyd, John P. 12 2006 Defeating the Runge phenomenon for equispaced polynomial interpolation via Tikhonov regularization. Zbl 0760.65007Boyd, John P. 12 1992 Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals. Zbl 0666.65022Boyd, John P. 12 1987 Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding. Zbl 1110.65037Boyd, John P. 12 2006 Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\). Zbl 1159.65112Boyd, John P. 12 2009 Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval. Zbl 1207.41011Boyd, John P. 12 2010 The double cnoidal wave of the Korteweg-de Vries equation: An overview. Zbl 0558.35065Boyd, John P. 11 1984 The asymptotic Chebyshev coefficients for functions with logarithmic endpoint singularities: Mappings and singular basis functions. Zbl 0668.65017Boyd, John P. 11 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 0806.65146Boyd, John P. 11 1994 Error saturation in Gaussian radial basis functions on a finite interval. Zbl 1189.65023Boyd, John P. 11 2010 Finding the zeros of a univariate equation: Proxy rootfinders, Chebyshev interpolation, and the companion matrix. Zbl 1270.65023Boyd, John P. 11 2013 Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions. Zbl 1365.76208Boyd, John P.; Xu, Zhengjie 11 2011 Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation. Zbl 1163.74322Boyd, John P.; Chen, Guan-Yu 10 2002 Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations. Zbl 1022.35070Tan, Benkui; Boyd, John P. 10 2001 A Chebyshev polynomial interval-searching method (“Lanczos economization”) for solving a nonlinear equation with application to the nonlinear eigenvalue problem. Zbl 0823.65047Boyd, John P. 10 1995 Global approximations to the principal real-valued branch of the Lambert \(W\)-function. Zbl 0940.65018Boyd, J. P. 10 1998 A numerical comparison of seven grids for polynomial interpolation on the interval. Zbl 0949.65009Boyd, J. P. 10 1999 Accurate calculation of the solutions to the Thomas-Fermi equations. Zbl 1410.81015Amore, Paolo; Boyd, John P.; Fernández, Francisco M. 10 2014 Weakly nonlinear wavepackets in the Korteweg-de Vries equation: The KdV/NLS connection. Zbl 0980.35146Boyd, John P.; Chen, Guan-Yu 10 2001 The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation. With a foreword by John P. Boyd. Zbl 1342.41001Kowalenko, Victor 10 2009 Numerical study of elliptical modons using a spectral method. Zbl 0715.76007Boyd, John P.; Ma, Hong 9 1990 Polynomial series versus sinc expansions for functions with corner or endpoint singularities. Zbl 0608.65010Boyd, John P. 9 1986 A lag-average generalization of Euler’s method for accelerating series. Zbl 0838.65002Boyd, John P. 9 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 1006.65116Boyd, John P. 9 2002 The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. Zbl 1301.41003Boyd, John P.; Petschek, Rolfe 9 2014 New approximations to the principal real-valued branch of the Lambert \(W\)-function. Zbl 1381.33020Iacono, Roberto; Boyd, John P. 9 2017 Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the \(D_4\) symmetry group; interpolation within a squircle. I. Zbl 1349.65056Li, Shan; Boyd, John P. 9 2014 Asymptotic coefficients for Gaussian radial basis function interpolants. Zbl 1200.41001Boyd, John P.; Wang, Lei 9 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 0945.35086Tan, Benkui; Boyd, John P. 9 2000 Sum-accelerated pseudospectral methods: The Euler-accelerated sinc algorithm. Zbl 0726.65019Boyd, John P. 8 1991 Cnoidal waves as exact sums of repeated solitary waves: New series for elliptic functions. Zbl 0559.76019Boyd, John P. 8 1984 Large mode number eigenvalues of the prolate spheroidal differential equation. Zbl 1041.34080Boyd, John P. 8 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 1366.65009Boyd, John P.; Ong, Jun Rong 8 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 1027.65136Boyd, John P. 8 2003 A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. Zbl 1092.65020Boyd, John P. 7 2006 Chebyshev domain truncation is inferior to Fourier domain truncation for solving problems on an infinite interval. Zbl 0666.65099Boyd, John P. 7 1988 Chebyshev and Legendre spectral methods in algebraic manipulation languages. Zbl 0793.65084Boyd, John P. 7 1993 The arctan/tan and Kepler-Burgers mappings for periodic solutions with a shock, front, or internal boundary layer. Zbl 0760.65106Boyd, John P. 7 1992 High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. Zbl 1352.65458Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris 7 2016 Sum-accelerated pseudospectral methods: Finite differences and sech-weighted differences. Zbl 0845.65041Boyd, John P. 7 1994 Construction of Lighthill’s unitary functions: The imbricate series of unity. Zbl 0909.42004Boyd, John P. 7 1997 Near-corner waves of the Camassa-Holm equation. Zbl 1136.35445Boyd, John P. 7 2005 Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation. Zbl 1136.74330Boyd, John P. 7 2005 Optimal truncations for multivariate Fourier and Chebyshev series: mysteries of the hyperbolic cross. I: bivariate case. Zbl 1465.42004Zhang, Xiaolong; Boyd, John P. 1 2020 Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations. Zbl 06969471Zhang, Xiaolong; Boyd, John P. 4 2019 High order analysis of the limit cycle of the van der Pol oscillator. Zbl 1383.34076Amore, Paolo; Boyd, John P.; Fernández, Francisco M. 2 2018 New approximations to the principal real-valued branch of the Lambert \(W\)-function. Zbl 1381.33020Iacono, Roberto; Boyd, John P. 9 2017 All roots spectral methods: constraints, floating point arithmetic and root exclusion. Zbl 1358.65049Boyd, John P.; Gheorghiu, Călin-Ioan 1 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 1411.76112Boyd, John P. 1 2017 High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. Zbl 1352.65458Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris 7 2016 A degree-increasing [\(N\) to \(N+1\)] homotopy for Chebyshev and Fourier spectral methods. Zbl 1334.65122Boyd, John P. 3 2016 Tracing multiple solution branches for nonlinear ordinary differential equations: Chebyshev and Fourier spectral methods and a degree-increasing spectral homotopy [DISH]. Zbl 1371.65070Boyd, John P. 3 2016 Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: restrictions and two improvements. Zbl 1416.65478Huang, Zhu; Boyd, John P. 1 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 1443.65104Boyd, John P. 1 2016 RBF-vortex methods for the barotropic vorticity equation on a sphere. Zbl 1351.86009Xiao, Jianping; Wang, Lei; Boyd, John P. 4 2015 Simple analytic approximations for the Blasius problem. Zbl 1364.76040Iacono, R.; Boyd, John P. 3 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 1352.65566Huang, Zhu; Xiao, Jianping; Boyd, John P. 2 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 1352.65036Li, Shan; Boyd, John P. 2 2015 The Kidder equation: \(u_{xx}+2xu_x/\sqrt{1-\alpha u}=0\). Zbl 1327.65142Iacono, Roberto; Boyd, John P. 2 2015 Four ways to compute the inverse of the complete elliptic integral of the first kind. Zbl 1360.65080Boyd, John P. 1 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 1410.65015Boyd, John P. 1 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 1410.65022Li, Shan; Boyd, John P. 1 2015 Solving transcendental equations. The Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles. Zbl 1311.65047Boyd, John P. 29 2014 Accurate calculation of the solutions to the Thomas-Fermi equations. Zbl 1410.81015Amore, Paolo; Boyd, John P.; Fernández, Francisco M. 10 2014 The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. Zbl 1301.41003Boyd, John P.; Petschek, Rolfe 9 2014 Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the \(D_4\) symmetry group; interpolation within a squircle. I. Zbl 1349.65056Li, Shan; Boyd, John P. 9 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 1334.42011Boyd, John P. 1 2014 Rational Chebyshev series for the Thomas-Fermi function: endpoint singularities and spectral methods. Zbl 1260.65065Boyd, John P. 18 2013 Finding the zeros of a univariate equation: Proxy rootfinders, Chebyshev interpolation, and the companion matrix. Zbl 1270.65023Boyd, John P. 11 2013 The nonconvergence of \(h\)-refinement in prolate elements. Zbl 1282.65148Boyd, John P.; Gassner, Gregor; Sadiq, Burhan A. 5 2013 Hermite function interpolation on a finite uniform grid: defeating the Runge phenomenon and replacing radial basis functions. Zbl 1308.65019Boyd, John P.; Alfaro, Luis F. 3 2013 Quartic Gaussian and inverse-quartic Gaussian radial basis functions: the importance of a nonnegative Fourier transform. Zbl 1268.41014Boyd, John P.; McCauley, Philip W. 3 2013 A comparison of companion matrix methods to find roots of a trigonometric polynomial. Zbl 1349.65156Boyd, John P. 1 2013 A Fourier error analysis for radial basis functions on an infinite uniform grid. II: Spectral-plus is special. Zbl 1334.65036Boyd, John P. 1 2013 Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions. Zbl 1408.65070Boyd, John P.; Xu, Zhengjie 5 2012 Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind. Zbl 1243.65035Boyd, John P. 3 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 1311.42007Boyd, John P.; Xiu, Yang (Chris) 1 2012 One-point pseudospectral collocation for the one-dimensional Bratu equation. Zbl 1222.65070Boyd, John P. 29 2011 Numerical experiments on the condition number of the interpolation matrices for radial basis functions. Zbl 1208.65056Boyd, John P.; Gildersleeve, Kenneth W. 24 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 1210.65192Boyd, John P.; Yu, Fu 23 2011 Chebyshev spectral methods and the Lane-Emden problem. Zbl 1249.65158Boyd, John P. 17 2011 Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions. Zbl 1365.76208Boyd, John P.; Xu, Zhengjie 11 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 1366.65009Boyd, John P.; Ong, Jun Rong 8 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 1217.65037Boyd, John P. 5 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 1210.65029Boyd, John P. 5 2011 New series for the cosine lemniscate function and the polynomialization of the lemniscate integral. Zbl 1209.65028Boyd, John P. 3 2011 Six strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite interval. Zbl 1207.41011Boyd, John P. 12 2010 Error saturation in Gaussian radial basis functions on a finite interval. Zbl 1189.65023Boyd, John P. 11 2010 Asymptotic coefficients for Gaussian radial basis function interpolants. Zbl 1200.41001Boyd, John P.; Wang, Lei 9 2010 Sensitivity of RBF interpolation on an otherwise uniform grid with a point omitted or slightly shifted. Zbl 1193.65014Boyd, John P.; Bridge, Lauren R. 5 2010 The uselessness of the fast Gauss transform for summing Gaussian radial basis function series. Zbl 1180.65185Boyd, John P. 4 2010 The Legendre-Burgers equation: when artificial dissipation fails. Zbl 1342.76094Boyd, John P. 1 2010 Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. I: Single-interval schemes. Zbl 1364.65025Boyd, John P.; Ong, Jun Rong 31 2009 Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation. Zbl 1171.41004Boyd, John P.; Xu, Fei 28 2009 Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms. Zbl 1163.42001Boyd, John P. 15 2009 An analytic approximation to the cardinal functions of Gaussian radial basis functions on an infinite lattice. Zbl 1178.65012Boyd, John P.; Wang, Lei 14 2009 Truncated Gaussian RBF differences are always inferior to finite differences of the same stencil width. Zbl 1364.65262Boyd, John P.; Wang, Lei 13 2009 Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\). Zbl 1159.65112Boyd, John P. 12 2009 The Stokes phenomenon, Borel summation and Mellin-Barnes regularisation. With a foreword by John P. Boyd. Zbl 1342.41001Kowalenko, Victor 10 2009 Chebyshev expansion on intervals with branch points with application to the root of Kepler’s equation: A Chebyshev-Hermite-Padé method. Zbl 1152.65024Boyd, John P. 6 2009 Three ways to solve the Poisson equation on a sphere with Gaussian forcing. Zbl 1173.65068Boyd, John P.; Zhou, Cheng 2 2009 An SVD analysis of equispaced polynomial interpolation. Zbl 1175.65020Boyd, John P.; Sousa, Alan M. 1 2009 The Blasius function: computations before computers, the value of tricks, undergraduate projects, and open research problems. Zbl 1152.76024Boyd, John P. 25 2008 Evaluating of Dawson’s integral by solving its differential equation using orthogonal rational Chebyshev functions. Zbl 1157.65331Boyd, John P. 4 2008 Exploiting parity in converting to and from Bernstein polynomials and orthogonal polynomials. Zbl 1138.65024Boyd, John P. 3 2008 Kelvin waves in the nonlinear shallow water equations on the sphere: nonlinear travelling waves and the corner wave bifurcation. Zbl 1155.76013Boyd, John P.; Zhou, Cheng 2 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 1118.65032Boyd, John P.; Gally, Daniel H. 13 2007 Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid. Zbl 1152.65404Boyd, John P. 7 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 1121.65049Boyd, John P. 7 2007 Rootfinding for a transcendental equation without a first guess: polynomialization of Kepler’s equation through Chebyshev polynomial expansion of the sine. Zbl 1105.65054Boyd, John P. 6 2007 Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries. Zbl 1132.65039Boyd, John P. 4 2007 Planetary solitary waves. Zbl 1316.76023Boyd, J. P. 3 2007 Computing real roots of a polynomial in Chebyshev series form through subdivision. Zbl 1119.65033Boyd, John P. 17 2006 Asymptotic Fourier coefficients for a \(C^\infty\) bell (smoothed-“top-hat”) & the Fourier extension problem. Zbl 1105.65129Boyd, John P. 13 2006 Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves. Zbl 1090.65052Boyd, John P. 12 2006 Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding. Zbl 1110.65037Boyd, John P. 12 2006 A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. Zbl 1092.65020Boyd, John P. 7 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 1331.76082Boyd, John P. 3 2006 Rootfinding through global Newton iteration and Chebyshev polynomials for the amplitude of an electronic oscillator. Zbl 1106.65113Boyd, John P.; Visser, Robert M. 1 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 1079.35087Boyd, John P. 35 2005 Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. Zbl 1071.65189Boyd, John P. 32 2005 Algorithm 840: Computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions – prolate elements. Zbl 1070.65569Boyd, John P. 28 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 1061.65127Boyd, John P. 28 2005 Hyperasymptotics and the linear boundary layer problem: Why asymptotic series diverge. Zbl 1087.34032Boyd, John P. 14 2005 Near-corner waves of the Camassa-Holm equation. Zbl 1136.35445Boyd, John P. 7 2005 Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation. Zbl 1136.74330Boyd, John P. 7 2005 The cnoidal wave/corner wave/breaking wave scenario: a one-sided infinite-dimension bifurcation. Zbl 1070.35027Boyd, John P. 4 2005 A Chebyshev/rational Chebyshev spectral method for the Helmholtz equation in a sector on the surface of a sphere: defeating corner singularities. Zbl 1072.65153Boyd, John P. 2 2005 Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms. Zbl 1059.65024Boyd, John P. 50 2004 Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation. Zbl 1025.65042Boyd, John P. 47 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 1028.65086Boyd, John P.; Rangan, C.; Bucksbaum, P. H. 40 2003 Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions. Zbl 1031.65155Boyd, John P. 28 2003 Large mode number eigenvalues of the prolate spheroidal differential equation. Zbl 1041.34080Boyd, John P. 8 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 1027.65136Boyd, John P. 8 2003 A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds. Zbl 0999.65132Boyd, John P. 64 2002 Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding. Zbl 1034.65028Boyd, John P. 28 2002 Envelope solitary waves and periodic waves in the AB equations. Zbl 1114.76315Tan, Benkui; Boyd, John P. 13 2002 Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation. Zbl 1163.74322Boyd, John P.; Chen, Guan-Yu 10 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 1006.65116Boyd, John P. 9 2002 Shafer (Hermite-Padé) approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude. Zbl 1215.76017Boyd, John P.; Natarov, Andrei 3 2002 Nonlinear wave packets of equatorial Kelvin waves. Zbl 1206.76009Chen, Guan-Yu; Boyd, John P. 3 2002 Chebyshev and Fourier spectral methods. 2nd rev. ed. Zbl 0994.65128Boyd, John P. 676 2001 Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions. Zbl 0987.65122Boyd, J. P. 213 2001 ...and 73 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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 all top 5 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) Citations by Year