Boyd, J. P.: 1988c, The superiority of Fourier domain truncation to Chebyshev domain

truncation for solving problems on an in¬nite interval, Journal of Scienti¬c Computing

3, 109“120.

Boyd, J. P.: 1989a, Chebyshev and Fourier Spectral Methods, Springer-Verlag, New York. 792

pp.

Boyd, J. P.: 1989b, New directions in solitons and nonlinear periodic waves: Polycnoidal

waves, imbricated solitons, weakly non-local solitary waves and numerical boundary

value algorithms, in T.-Y. Wu and J. W. Hutchinson (eds), Advances in Applied Mechan-

ics, number 27 in Advances in Applied Mechanics, Academic Press, New York, pp. 1“82.

Boyd, J. P.: 1989c, Periodic solutions generated by superposition of solitary waves for the

quarticly nonlinear Korteweg-de Vries equation, ZAMP 40, 940“944. Imbrication of

solitary wave generates good approximate periodic solutions.

Boyd, J. P.: 1989d, The asymptotic Chebyshev coef¬cients for functions with logarithmic

endpoint singularities, Applied Mathematics and Computation 29, 49“67.

Boyd, J. P.: 1989e, Non-local equatorial solitary waves, in J. C. J. Nihoul and B. M. Jamart

(eds), Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence: Proc. 20th Liege

Coll. on Hydrodynamics, Elsevier, Amsterdam, pp. 103“112.

Boyd, J. P.: 1990a, The orthogonal rational functions of Higgins and Christov and Cheby-

shev polynomials, Journal of Approximation Theory 61, 98“103.

Boyd, J. P.: 1990b, A numerical calculation of a weakly non-local solitary wave: the φ4

breather, Nonlinearity 3, 177“195.

Boyd, J. P.: 1990c, The envelope of the error for Chebyshev and Fourier interpolation, Jour-

nal of Scienti¬c Computing 5, 311“363.

Boyd, J. P.: 1990d, A Chebyshev/radiation function pseudospectral method for wave scat-

tering, Computers in Physics 4, 83“85.

Boyd, J. P.: 1991a, A comparison of numerical and analytical methods for the reduced wave

equation with multiple spatial scales, Applied Numerical Mathematics 7, 453“479.

Boyd, J. P.: 1991b, Monopolar and dipolar vortex solitons in two space dimensions, Wave

Motion 57, 223“243.

Boyd, J. P.: 1991c, Nonlinear equatorial waves, in A. R. Osborne (ed.), Nonlinear Topics of

Ocean Physics: Fermi Summer School, Course LIX, North-Holland, Amsterdam, pp. 51“

97.

BIBLIOGRAPHY 599

Boyd, J. P.: 1991d, Weakly nonlocal solitary waves, in A. R. Osborne (ed.), Nonlinear Topics of

Ocean Physics: Fermi Summer School, Course LIX, North-Holland, Amsterdam, pp. 527“

556.

Boyd, J. P.: 1991e, Weakly nonlocal solitons for capillary-gravity waves: Fifth-degree

Korteweg-de Vries equation, Physica D 48, 129“146.

Boyd, J. P.: 1991f, Sum-accelerated pseudospectral methods: The Euler-accelerated sinc

algorithm, Applied Numerical Mathematics 7, 287“296.

Boyd, J. P.: 1992a, The arctan/tan and Kepler-Burger mappings for periodic solutions with

a shock, front, or internal boundary layer, Journal of Computational Physics 98, 181“193.

Numerical trick which is useful for solitary waves and cnoidal waves.

Boyd, J. P.: 1992b, The energy spectrum of fronts: The time evolution of shocks in Burgers™

equation, Journal of the Atmospheric Sciences 49, 128“139.

Boyd, J. P.: 1992c, Multipole expansions and pseudospectral cardinal functions: A new

generalization of the Fast Fourier Transform, Journal of Computational Physics 102, 184“

186.

Boyd, J. P.: 1992d, A fast algorithm for Chebyshev and Fourier interpolation onto an irreg-

ular grid, Journal of Computational Physics 103, 243“257.

Boyd, J. P.: 1992e, Defeating the Runge phenomenon for equispaced polynomial interpola-

tion via Tikhonov regularization, Applied Mathematics Letters 5, 57“59.

Boyd, J. P.: 1993, Chebyshev and Legendre spectral methods in algebraic manipulation

languages, Journal of Symbolic Computing 16, 377“399.

Boyd, J. P.: 1994a, Hyperviscous shock layers and diffusion zones: Monotonicity, spectral

viscosity, and pseudospectral methods for high order differential equations, Journal of

Scienti¬c Computing 9, 81“106.

Boyd, J. P.: 1994b, The rate of convergence of Fourier coef¬cients for entire functions of in¬-

nite order with application to the Weideman-Cloot sinh-mapping for pseudospectral

computations on an in¬nite interval, Journal of Computational Physics 110, 360“372.

Boyd, J. P.: 1994c, The slow manifold of a ¬ve mode model, Journal of the Atmospheric Sci-

ences 51, 1057“1064.

Boyd, J. P.: 1994d, Nonlocal modons on the beta-plane, Geophysical and Astrophysical Fluid

Dynamics 75, 163“182.

Boyd, J. P.: 1994e, Time-marching on the slow manifold: The relationship between the

nonlinear Galerkin method and implicit timestepping algorithms, Applied Mathematics

Letters 7, 95“99.

Boyd, J. P.: 1994f, Sum-accelerated pseudospectral methods: Finite differences and sech-

weighted differences, Computer Methods in Applied Mechanics and Engineering 116, 1“11.

Boyd, J. P.: 1995a, Weakly nonlocal envelope solitary waves: Numerical calculations for the

Klein-Gordon (φ4 ) equation, Wave Motion 21, 311“330.

Boyd, J. P.: 1995b, A hyperasymptotic perturbative method for computing the radiation

coef¬cient for weakly nonlocal solitary waves, Journal of Computational Physics 120, 15“

32.

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Boyd, J. P.: 1995c, Eight de¬nitions of the slow manifold: Seiches, pseudoseiches and expo-

nential smallness, Dynamics of Atmospheres and Oceans 22, 49“75.

Boyd, J. P.: 1995d, A lag-averaged generalization of Euler™s method for accelerating series,

Applied Mathematics and Computation 72, 146“166.

Boyd, J. P.: 1995e, A Chebyshev polynomial interval-searching method (“Lanczos econo-

mization”) for solving a nonlinear equation with application to the nonlinear eigen-

value problem, Journal of Computational Physics 118, 1“8.

Boyd, J. P.: 1995f, Multiple precision pseudospectral computations of the radiation coef-

¬cient for weakly nonlocal solitary waves: Fifth-Order Korteweg-deVries equation,

Computers in Physics 9, 324“334.

Boyd, J. P.: 1996a, Asymptotic Chebyshev coef¬cients for two functions with very rapidly

or very slowly divergent power series about one endpoint, Applied Mathematics Letters

9(2), 11“15.

Boyd, J. P.: 1996b, Traps and snares in eigenvalue calculations with application to pseu-

dospectral computations of ocean tides in a basin bounded by meridians, Journal of

Computational Physics 126, 11“20. Corrigendum, 136, no. 1, 227-228 (1997).

Boyd, J. P.: 1996c, Numerical computations of a nearly singular nonlinear equation: Weakly

nonlocal bound states of solitons for the Fifth-Order Korteweg-deVries equation, Jour-

nal of Computational Physics 124, 55“70.

Boyd, J. P.: 1996d, The Erfc-Log ¬lter and the asymptotics of the Vandeven and Euler se-

quence accelerations, in A. V. Ilin and L. R. Scott (eds), Proceedings of the Third Interna-

tional Conference on Spectral and High Order Methods, Houston Journal of Mathematics,

Houston, Texas, pp. 267“276.

Boyd, J. P.: 1997a, Pad´ approximant algorithm for solving nonlinear ODE boundary value

e

broblems on an unbounded domain, Computers and Physics 11(3), 299“303.

Boyd, J. P.: 1997b, Pseudospectral/Delves-Freeman computations of the radiation coef¬-

cient for weakly nonlocal solitary waves of the Third Order Nonlinear Schroedinger

Equation and their relation to hyperasymptotic perturbation theory, Journal of Compu-

tational Physics 138, 665“694.

Boyd, J. P.: 1997c, The periodic generalization of Camassa-Holm “peakons”: An exact

superposition of solitary waves, Applied Mathematics and Computation 81(2), 173“187.

Classical solitons.

Boyd, J. P.: 1997d, Construction of Lighthill™s unitary functions: The imbricate series of

unity, Applied Mathematics and Computation 86, 1“10.

Boyd, J. P.: 1998a, Radiative decay of weakly nonlocal solitary waves, Wave Motion 27, 211“

221.

Boyd, J. P.: 1998b, Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics: Gener-

alized Solitons and Hyperasymptotic Perturbation Theory, Vol. 442 of Mathematics and Its

Applications, Kluwer, Amsterdam. 608 pp. Three chapters on spectral methods, solv-

ing spectral-discretized nonlinear equations, and special methods for nonlocal solitary

waves and other phenomena that radiate to spatial in¬nity.

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Boyd, J. P.: 1998c, High order models for the nonlinear shallow water wave equations on

the equatorial beta-plane with application to Kelvin wave frontogenesis, Dynamics of

Atmospheres and Oceans 28(2), 69“91.

Boyd, J. P.: 1998d, Two comments on ¬ltering, J. Comput. Phys. 143(1), 283“288. Shows

how to apply ¬lters or sum acceleration methods to spectral series so as to preserve

the boundary conditions. Also explains why additional boundary conditions are not

needed: high order ¬ltering operators can be interpreted as powers of the Legendre

or Chebyshev differential operator, which is singular at the boundaries.

Boyd, J. P.: 1998e, Global approximations to the principal real-valued branch of the Lambert

W-function, Appl. Math. Lett. 11(6), 27“31.

Boyd, J. P.: 1999a, Chebyshev and Fourier Spectral Methods, 2d edn, Dover, Mineola, New

York. 665 pp. Heavily revised and updated second edition of Boyd(1989).

Boyd, J. P.: 1999b, A numerical comparison of seven grids for polynomial interpolation on

the interval, Comput. Math. Appl. Submitted.

Boyd, J. P.: 1999c, The Blasius function in the complex plane, J. Experimental Math. In press.

Boyd, J. P.: 2001, Essays on Chebyshev and Fourier Spectral Methods. To appear.

Boyd, J. P. and Christidis, Z. D.: 1982, Low wavenumber instability on the equatorial beta-

plane, Geophysical Research Letters 9, 769“772.

Boyd, J. P. and Christidis, Z. D.: 1983, Instability on the equatorial beta-plane, in J. Nihoul

(ed.), Hydrodynamics of the Equatorial Ocean, Elsevier, Amsterdam, pp. 339“351.

Boyd, J. P. and Christidis, Z. D.: 1987, The continuous spectrum of equatorial Rossby waves

in a shear ¬‚ow, Dynamics of Atmospheres and Oceans 11, 139“151.

Boyd, J. P. and Flyer, N.: 1999, Compatibility conditions for time-dependent partial differ-

ential equations and the the rate of convergence of Chebyshev and Fourier spectral

methods, Comput. Meths. Appl. Mech. Engrg. In press.

Boyd, J. P. and Haupt, S. E.: 1991, Polycnoidal waves: Spatially periodic generalizations of

multiple solitary waves, in A. R. Osborne (ed.), Nonlinear Topics of Ocean Physics: Fermi

Summer School, Course LIX, North-Holland, Amsterdam, pp. 827“856.

Boyd, J. P. and Ma, H.: 1990, Numerical study of elliptical modons by a spectral method,

Journal of Fluid Mechanics 221, 597“611.

Boyd, J. P. and Natarov, A.: 1998, A Sturm-Liouville eigenproblem of the Fourth Kind:

A critical latitude with equatorial trapping, Stud. Appl. Math. 101, 433“455. Rational

TB calculation of logarithmically singular eigenproblems along an in¬nite interval

parallel to the real axis, but shifted from it by a constant.

Boyd, J. P. and Tan, B.: 1998, Vortex crystals and non-existence of non-axisymmetric soli-

tary waves in the Flierl-Petviashvili equation, Chaos, Solitons and Fractals 9, 2007“2021.

Double Fourier algorithm for a generalized, two-dimensional quasi-geostrophic equa-

tion.

Boyd, J. P. and Tan, B.: 1999, Composite bound states of wide and narrow envelope soli-

tons in the Coupled Schroedinger equations through matched asymptotic expansions,

Nonlinearity. Submitted.

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for nonperiodic boundary conditions with subtractions to improve convergence and

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e

Galerkin dans l™´ tude de stabilit´ des mouvements de convection naturelle. Probl` me

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Cornelius Lanczos International Centenary Conference, Society for Industrial and Applied

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cal methods for solving differential equations on the sphere, Monthly Weather Review

117, 1058“1075. Spherical harmonics versus fourth and sixth order ¬nite differences.

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bolic problems, Comput. & Math. Applics. 24, 37“49.

Cai, W., Gottlieb, D. and Shu, C.: 1989, Essentially nonoscillatory spectral Fourier methods

for shock wave calculation, Mathematics of Computation 52(186), 389“410.

Cai, W., Gottlieb, D. and Shu, C. W.: 1992b, On one-sided ¬lters for spectral Fourier approx-

imation of discontinuous functions, SIAM Journal of Numerical Analysis 29, 905“916.

Cain, A. B., Ferziger, J. H. and Reynolds, W. C.: 1984, Discrete orthogonal function expan-

sions for non-uniform grids using the Fast Fourier transform, Journal of Computational

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Chebyshev.

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stants, Proceedings IEEE 55, 2016“2017. Not spectral; higher order Pad´ time marching

e

scheme.

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Canuto, C. and Funaro, D.: 1988, The Schwarz algorithm for spectral methods, SIAM Jour-

nal of Numerical Analysis 25, 24“40.

Canuto, C. and Quarteroni, A.: 1985, Preconditioned minimal residual methods for Cheby-

shev spectral calculations, Journal of Computational Physics 60, 315“337.

Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A.: 1988, Spectral Methods for Fluid

Dynamics, Springer-Verlag, New York. Classic text, 556 pp. Very comprehensive and

readable, now in paperback.

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and Y. Maday (eds), Analysis, Algorithms and Applications of Spectral and High Order

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ference on Spectral and High Order Methods (ICOSAHOM ™92), Le Corum, Montpel-