Curriculum Vita: John P. Boyd

Address:
Department of Atmospheric, Oceanic & Space Science
2455 Hayward Avenue
Ann Arbor, MI 48109

Internet: jpboyd@engin.umich.edu

Homepage: http:/www-personal.engin.umich:/~jpboyd

Phone: (734) 764-3338 FAX: (734) 764-5137

Education: Ph. D., Harvard, 1976
S. M., Harvard, 1975
A. B., Harvard, 1973

Positions: Professor, Univ. of Michigan, 1988-
& Associate Director, Laboratory for Scientific Computation, 1986-
Visiting Professor, Rutgers, 1991-1992
Acting Director, 1989

Associate Professor, Univ. of Michigan, 1982-1988
Assistant Professor, Univ. of Michigan 1977-1982
Visiting Research Associate (on leave), Harvard, 1980
Postdoctoral Scholar, Univ. of Michigan, 1977
Postdoctoral Fellow, National Center for Atmospheric Research, 1976

Professional American Meteorological Society
Societies: Society for Industrial and Applied Mathematics
American Geophysical Union

Honors: Phi Beta Kappa
UCAR Graduate Fellowship
NCAR Postdoctoral Fellowship

BOOKS
Chebyshev and Fourier Spectral Methods, Springer-Verlag, 792 pp. (1989)
(Second edition, Dover Press, June, 2000).
The new edition will contain an index and several chapters of new material as well as over 800 references.)

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics, Kluwer, 610 pp., (1998)

ARTICLES

1. "The Noninteraction of Waves with the Zonally Averaged Flow on a Spherical Earth and the Interrelationships of Eddy Fluxes of Heat, Energy, and Momentum", . Atmos. Sci., 33, 2285-2291 (1976).
2. "A Chebyshev Polynomial Method for Computing Analytic Solutions to Eigenvalue Problems with Application to the Anharmonic Oscillator", J. Math. Phys., 19, 1445-1456 (1978).
3. "The Choice of Spectral Functions on a Sphere For Boundary and Eigenvalue Problems: A Comparison of Chebyshev, Fourier, and Associated Legendre Expansions," Mon. Weath. Rev., 106, 1184-1191 (1978).
4. "Spectral and Pseudospectral Methods for Eigenvalue and Nonseparable Boundary Value Problems," Mon. Weath. Rev., 106, 1192-1203 (1978).
5. "The Effects of Latitudinal Shear on Equatorial Waves, Part I: Theory and Methods," J. Atmos. Sci., 35, 2236-2258 (1978).
6. "The Effects of Latitudinal Shear on Equatorial Waves, Part II: Applications to the Atmosphere," J. Atmos. Sci., 35, 2259-2267 (1978).
7. "The Nonlinear Equatorial Kelvin Wave," J. Phys. Oceangr., 10, 1-11 (1980).
8. "The Rate of Convergence of Hermite Function Series," Math. Comp., 35, 1309-1316 (1980).
9. "Equatorial Solitary Waves, Part I: Rossby Solitons,", J. Phys. Oceangr., 10, 1699-1718 (1980).
10. "A Sturm-Liouville Eigenproblem with an Interior Pole," J. Math. Phys., 22, 1575-1590 (1981).
11. "The Rate of Convergence of Chebyshev Polynomials for Functions Which Have Asymptotic Power Series About One Endpoint," Math. Comp., 37, 189-196 (1981).
12. "Analytical Approximations to the Modon Dispersion Relation", Dyn. Atmos. Oceans, 6, 97-101 (1981).
13. "The Optimization of Convergence for Chebyshev Polynomial Methods in an Unbounded Domain," J. Comp. Phys., 45, 43-79 (1982).
14. "The Effects of Meridional Shear on Planetary Waves, Part I: Nonsingular Profiles," J. Atmos. Sci., 39, 756-769 (1982).
15. "The Effects of Meridional Shear on Planetary Waves, Part II: Critical Latitudes. J. Atmos. Sci., 39, 770-790 (1982).
16. "A Chebyshev Polynomial Rate-of-Convergence Theorem for Stieltjes Functions," Math. Comp., 39, 201-206 (1982).
17. "Theta Functions, Gaussian Series, and Spatially Periodic Solutions of the Korteweg-deVries Equation," J. Math. Phys., 23, 375-387 (1982).
18. "Low Wavenumber Instability on the Equatorial Beta-Plane," with Z. D. Christidis, Geophys. Res. Lett., 9, 769-772 (1982).
19. "Equatorial Solitary Waves, Part II: Envelope Solitons," J. Phys. Oceangr., 13, 428-449 (1983).
20. "Long Wave/Short Wave Resonance in Equatorial Waves," J. Phys. Oceangr., 13, 450-458 (1983).
21. "Second Harmonic Resonance for Equatorial Waves," J. Phys. Oceangr., 13, 459-466 (1983).
22. "Instability on the Equatorial Beta-Plane," with Z. D. Christidis, in Hydrodynamics of the Equatorial Ocean, ed. by J. Nihoul, Elsevier, Amsterdam, 339-351 (1983).
23. "The Continuous Spectrum of Linear Couette Flow with the Beta Effect," J. Atmos. Sci., 40, 2304-2308 (1983).
24. "The Asymptotic Coefficients of Hermite Series," J. Comp. Phys., 54, 382-410 (1984).
25. "Equatorial Solitary Waves, Part 4: Kelvin Solitons in a Shear Flow," Dyn. Atmos. Oceans, 8, 173-184 (1984).
26. "Cnoidal Waves as Exact Sums of Repeated Solitary Waves: New Series for Elliptic Functions," SIAM J. Appl. Math., 44, 952-955 (1984).
27. "The Double Cnoidal Wave of the Korteweg-deVries Equation: An Overview," J. Math. Phys., 25, 3390-3401 (1984).
28. "Perturbation Theory for the Double Cnoidal Wave of the "Korteweg-deVries Equation," J. Math. Phys., 25, 3402-3414 (1984).
29. "The Special Modular Transformation for Polycnoidal Waves of the Korteweg-deVries Equation," J. Math. Phys., 25, 3415-3423 (1984).
30. "Complex Coordinate Methods for Hydrodynamic Instabilities and Sturm-Liouville Eigenproblems with an Interior Singularity," J. Comp. Phys., 57, 454-471 (1985).
31. "Equatorial Solitary Waves, Part 3: Modons," J. Phys. Oceangr., 15, 46-54 (1985).
32. "Solitons from Sine Waves: Analytical and Numerical Methods for Non-Integrable Solitary and Cnoidal Waves," Physica 21D, 227-246 (1986).
33. "Summability Methods for Hermite Functions," with D. W. Moore Dyn. Atmos. Sci, 10, 51-62 (1986).
34. "Solitons in a Continuously Stratified Equatorial Ocean," with H. G. Marshall, J. Phys. Oceangr., 17, 1016-1031 (1987).
35. "The Continuous Spectrum of Equatorial Rossby Waves in a Shear Flow," with Z. D. Christidis, Dyn. Atmos. Oceans., 11, 139-151 (1987).
36. "Barotropic Equatorial Waves: the Non-Uniformity of the Equatorial Beta-Plane," J. Atmos. Sci., 42, 1965-1967 (1985).
37. "Polynomial Series versus Sinc Expansions for Functions with Corner or Endpoint Singularities," J. Comp. Phys., 64, 266-269 (1986).
38. "The Orthogonal Rational Functions of Higgins & Christov and Chebyshev Polynomials", J. Approx. Theor., 61, 98-103 (1990).
39. "Spectral Methods Using Rational Basis Functions on an Infinite Interval", J. Comp. Phys., 69, 112-142 (1987).
40. "Orthogonal Rational Functions on a Semi-Infinite Interval", J. Comp. Phys., 70, 63-88 (1987).
41. "The Arctan/Tan & Kepler-Burgers Mapping for Periodic Solutions with a Shock, Front, or Internal Boundary Layer", J. Comp. Phys., 98, 181-193 (1992)
42. "Energetics Analysis of a Multilevel Global Spectral Model. Part I: Balanced Energy and Transient Energy", with S.-D. Ko and J. J. Tribbia, Mon. Weath. Rev., 117, 1941-1953 (1989).
43. "An Analytical and Numerical Study of the Two-Dimensional Bratu Equation", J. Scientific Computing, 1, 183-206 (1986).
44. "Energetics of a Multilevel Global Spectral Model. Part II: Zonal and Meridional Gravitational Energy", with S.-D. Ko and J. J. Tribbia, Mon. Weath. Rev., 117, 1954-1964 (1989).
45. "Exponentially Convergent Fourier/Chebyshev Quadrature Schemes on Bounded & Infinite Intervals, J. Scientific Computing, 2, 99-109 (1987).
46. "Periodic Solutions Generated by Solitons for the Quartically Nonlinear Korteweg-deVries Equation", ZAMP, 40, 940-944 (1989).
47. "Modeling Nonlinear Resonance: A Modification to the Stokes' Perturbation Expansion", with S. E. Haupt, Wave Motion, 10, 83-98 (1988).
48. "Summation Methods & Pseudospectral Algorithms, Part I: Finite Difference Summation of Whittaker Cardinal (Sinc) Series, submitted to J. Comp. Phys. (1987).
49. "A Comparison of Numerical & Analytical Methods for the Reduced Wave Equation with Multiple Spatial Scales", Appl. Numer. Math, 7, 453-479 (1991).
50. "Chebyshev Domain Truncation Is Inferior to Fourier Domain Truncation for Solving Problems on an Infinite Interval", J. Scient. Comp., 3, 109-120 (1988).
51. "The Asymptotic Chebyshev Coefficients for Functions with Logarithmic Endpoint Singularities", Appl. Math. & Computation, 29, 49-67 (1989).
52. "Chebyshev Pseudospectral Method for Viscous Flows with Corner Singularities", with N. Y. Lee and W. W. Schultz, J. Scientific Computing, 4, 1-24 (1989).
53. "Stability of Fluid in a Rectangular Enclosure by Spectral Method", with N. Y. Lee and W. W. Schultz, Int. J. Heat and Mass Transfer, 32, 513-520 (1989).
54. "Numerical Calculation of a Weakly Non-Local Solitary Wave: The "Breather" of the Field Theory", Nonlinearity, 3, 177-195 (1990).
55. "Chebyshev and Legendre Spectral Methods in Algebraic Manipulation Languages", J. Symbolic Computing, 16, 377-399 (1993).
56. An Analytical Solution for a Nonlinear Differential Equation with Logarithmic Decay", Adv. Applied Math., 9, 358-363 (1988).
57. "Monopolar & Dipolar Vortex Solitons in Two Space Dimensions", Wave Motion, 57, 223-243 (1991).
58. "Double Cnoidal Waves of the Korteweg-deVries Equation: The Boundary Value Approach", with S. E. Haupt, Physica D50, 117-134 (1991).
59. "Weakly Non-Local Solitary Waves". In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence: Proceedings of the Twentieth Hydrodynamics Colloquium, ed. by J. C. J. Nihoul & B. M. Jamart, Elsevier, Amsterdam, 103-112 (1989).
60. "Nonlinear equatorial Waves". In Nonlinear Topics of Ocean Physics, Proceedings of the Fermi Summer School, Course 109, ed. by A. R. Osborne and L. Bergamasco. North-Holland, Amsterdam, 51-97 (1991).
61. "Polycnoidal Waves: Spatially Periodic Generalizations Multiple Solitons." With S. E. Haupt. In Nonlinear Topics of Ocean Physics, ed. by A. R. Osborne and L. Bergamasco. North-Holland, Amsterdam, 827-856 (1991).
62. "Weakly Non-Local Solitary Waves". In Nonlinear Topics of Ocean Physics, ed. by A. R. Osborne and L. Bergamasco. North-Holland, Amsterdam, 527-556 (1991).
63. "The Envelope of the Error for Chebyshev & Fourier Interpolation", J. Scientific Computing, 5, 311-363 (1990).
64. "New Directions in Solitons and Nonlinear Periodic Waves: Polycnoidal Waves, Imbricated Solitons, Weakly Non-Local Solitary Waves & Numerical Boundary Value Algorithms", In Advances in Applied Mechanics, 27, ed. by T.-Y. Wu and J. W. Hutchinson, 1-82 (1989).
65. "Numerical Study of Elliptical Modons by a Spectral Method", with H. Ma. J. Fluid Mech., 221, 597-611 (1990).
66. "Weakly Non-Local Solitons for Capillary-Gravity Waves: The Fifth-Degree Korteweg-deVries Equation". Physica D, 48, 129-146 (1991).
67. "A Chebyshev/Radiation Function Pseudospectral Method for Wave Scattering". Computers in Physics, 4, 83-85 (1990).
68. "Spectral Method Solution of the Stokes Equations on Nonstaggered Grids", with M. Schumack and W. W. Schulz. J. Comp. Phys., 94, 30-58 (1991).
69. "The Energy Spectrum of Fronts: The Time Evolution of Shocks in Burger's Equation", J. Atmos. Sci., 49, 128-139 (1992).
70. "Sum-Accelerated Pseudospectral Methods: The Euler- Accelerated Sinc Algorithm", Appl. Numer. Math., 7, 287-296 (1991).
71. "Multipole Expansions & Pseudospectral Cardinal Functions: A New Generalization of the Fast Fourier Transform", J. Comp. Phys., 102, 184-186 (1992).
72. "A Fast Algorithm for Chebyshev, Fourier & Sinc Interpolation Onto an Irregular Grid", J. Comp. Phys., 103, 243-257 (1992).
73. "Hyperviscous Shock Layers and Diffusion Zones: Monotonicity, Spectral Viscosity, and Pseudospectral Methods for Very High Order Differential Equations". J. Sci. Comput. 9, 81-106 (1994).
74. "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", J. Comp. Phys., 110, 360-372 (1994).
75. "Taylor Vortices Between Elliptical Cylinders", with M. Schumack and W. W. Schultz, Phys. Fluids, 4, 2578-2581 (1992).
76. "Weakly Nonlocal Envelope Solitary Waves: Numerical Calculations for the Klein-Gordon (f4) Equation". Wave Motion, 21, 311-330 (1992).
77. "Nonlocal Modons on the Beta-Plane". Geophys. Astrophys. Fluid Dyn., 75, 163-182 (1994).
78. "Eight Definitions of the Slow Manifold: Seiches, Pseudoseiches and Exponential Smallness", Dyn. Atmos. Oceans, 22, 49-75 (1995).
79. "Defeating the Runge Phenomenon for Equispaced Polynomial Interpolation via Tikhonov Regularization." Appl. Math. Lett. 5, 57-59 (1992).
80. "A Lag-Averaged Generalization of Euler's Method for Accelerating Series". Appl. Math. & Comput., 72, 143-166 (1995).
81. "Sum-Accelerated Pseudospectral Methods: Finite Differences & Sech-Weighted Differences. Comp. Meths. Appl. Mech. Eng., 116, 1-11 (1994).
82. "The Slow Manifold of a Five-Mode Model". J. Atmos. Sci. 51, 1057-1064 (1994).
83. "Time-Marching on the Slow Manifold: The Relationship Between the Nonlinear Galerkin Method and Implicit Timestepping Algorithms". Appl. Math. Lett., 7, 95-99 (1994).
84. "Numerical Computations of a Nearly Singular Nonlinear Equation: Weakly Nonlocal Bound States of Solitons for the Fifth-Order Korteweg-deVries Equation". In press, J. Comp. Phys., 124, 55-70 (1996).
85. "Multiple Precision Pseudospectral Computations of the Radiation Coefficient for Weakly Nonlocal Solitary Waves: Fifth-Order Korteweg-DeVries Equation". Computers in Physics, 9, 324-334 (1995).
86. "A Chebyshev Polynomial Interval-Searching Method ("Lanczos Economization") for Solving a Nonlinear Equation with Application to the Nonlinear Eigenvalue Problem", J. Comp. Phys., 118, 1-8 (1995).
87. "A Staggered Spectral Finite Element Method for the Shallow Water Equations", with M. Iskandarani and D. Haidvogel. Int. J. Num. Meths. Fluids, 20, 393-414 (1995).
88. "The Periodic Generalization of Camassa-Holm "Peakons": An Exact Superposition of Solitary Waves". Submitted to Appl. Math. Comput. (1995)
. 89. "The Erfc-Log Filter and the Asymptotics of the Euler and Vandeven Sum Accelerations", in Proceedings of the Third International Conference on Spectral and High Order Methods, ed. by A. V. Ilin and L. R. Scott, Houston J. Mathematics, Houston, Texas , 267-276 (1996).
90. "A Hyperasymptotic Perturbative Method for Computing the Radiation Coefficient for Weakly Nonlocal Solitary Waves". J. Comp. Phys., 120, 15-32 (1995).
91. "Spectral Elements Methods on Triangles for Geophysical Fluid Dynamics", with B. A. Wingate, in Proceedings of the Third International Conference on Spectral and High Order Methods, ed. by A. V. Ilin and L. R. Scott, Houston J. Mathematics, Houston, Texas , 267-276 (1996).
92. "The Devil's Invention: Asymptotics, Superasymptotics and Hyperasymptotics", Acta Applicandae, 56, 1-98 (1999).
93. "Radiative Decay of Weakly Nonlocal Solitary Waves", Wave Motion, 27, 211-221 (1998).
94. "Asymptotic Chebyshev Coefficients for Two Functions with Very Rapidly or Very Slowly Divergent Power Series About One Endpoint", Applied Mathematics Letters, 9, No.2, 11-15, (1996).
95. "Traps and Snares in Eigenvalue Calculations with Application to Pseudospectral Computations of Ocean Tides in a Basin Bounded by Meridians". J. Comput. Phys. , 126, 11-20 (1996). Corrigendum, 136, no. 1, 227-228 (1997).
96. "Spectral Modeling of Nonlinear Dispersive Waves", with B. F. Sanders and N. D. Katopodes. J. Hydraulic Eng. of ASCE, 124, 2-12 (1998).
97. "Short Wave Behavior of Long Wave Equations", with N. D. Katopodes and B. F. Sanders. J. of Waterways, Ports, Coastal and Ocean Eng. of ASCE, 124 (5), 238-247 (1998).
98. "High Order Models for the Nonlinear Shallow Water Wave Equations on the Equatorial Beta-plane with Application to Kelvin Wave Frontogenesis", Dyn. Atmos. Oceans., 28, no. 2, 69-91 (1998).
99. "Construction of Lighthill's Unitary Functions: The Imbricate Series of Unity". Appl. Math. Comput., 86, 1-10 (1997).
100. "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", J. Comput. Phys., 143, no. 1, 283-288 (1998).
101. "Dynamics of the Flierl-Petviashvili Monopoles in a Barotropic Model with Topographic Forcing", with Benkui Tan, Wave Motion, 26, 239-252 (1997).
102. "Pseudospectral/Delves-Freeman computations of the radiation coefficient for weakly nonlocal solitary waves of the Third Order Nonlinear Schroedinger Equation and their relation to hyperasymptotic perturbation theory", J. Comput. Phys., 138, No. 2., 665-694 (1997).
103. "Pad Approximant Algorithm for Solving Nonlinear ODE Boundary Value Problems on an Unbounded Domain", Computers in Physics, 11, no. 3 (May-June), 299-303 (1997).
104. "Vortex Crystals and Non-existence of Non-axisymmetric Solitary Waves in the Flierl-Petviashvili Equation", with B. Tan, Chaos, Solitons & Fractals, 9, no. 12, 2007-2021 (1998).
105. "Compatibility Conditions for Time-Dependent Partial Differential Equations and the Rate of Convergence of Chebyshev and Fourier Spectral Methods", with N. Flyer, Comput. Meths. Appl. Mech. Eng., 175, 281--309 (1999).
106. "A Sturm-Liouville Eigenproblem of the Fourth Kind: A Critical Latitude with Equatorial Trapping", with A. Natarov, Stud. Appl. Math., 101, 433-455 (1998).
107. "Global approximations to the principal real-valued branch of the Lambert W-function". Appl. Math. Lett., 11, no. 6, 27-31 (1998).
108. "Davydov Soliton Collisions", with Benkui Tan, Physics Letters A., 240, 282-286 (1998).
109. "The Blasius Function in the Complex Plane", in proof, Journal of Experimental Math., 8, no. 4 (1999).
110. "Propagation of Nonlinear Kelvin Wave Packet in the Equatorial Ocean", with G.-Y. Chen, submitted to J. Phys. Oceangr., (1997). 111. "Analytical and Numerical Studies of Weakly Nonlocal Solitary Waves of the Rotation-Modified Korteweg-deVries Equation, with G.-Y. Chen, submitted to Dyn. Atmos. Oceans (1999).
112. "A Numerical Comparison of Seven Grids for Polynomial Interpolation on the Interval", Computers and Mathematics with Applications, 38, 35-50 (1999).
113. "Coupled-Mode Envelope Solitary Waves in a Pair of Cubic Schroedinger Equations with Cross Modulation: Analytical Solution and Collisions",, with Benkui Tan, in proof Chaos, Solitons and Fractals (1999).
114. "Composite Bound States of Wide and Narrow Envelope Solitons in the Coupled Schroedinger Equations Through Matched Asymptotic Expansions", with Benkui Tan, Nonlinearity, 12, 1449-1469 (1999).
115. "Beyond-all-orders Instability in the Equatorial Kelvin Wave", with Andrei Natarov, submitted to Dyn. Atmos. Oceans (1999).
116. "Rational Chebyshev Spectral Methods for Unbounded Solutions on an Infinite Interval using Polynomial- Growth Special Basis Functions", submitted to Computers and Mathematics with Applications, (1999).
117. "Five Regimes of the Quasi-Cnoidal, Steadily-Translating Waves of the Rotation-Modified Korteweg-deVries ("Ostrovsky") Equation", with G.-Y. Chen, submitted to Wave Motion (1999).
118. "Shafer (Hermite-Pade) Approximants for Functions with Exponentially Small Imaginary Part with Application to Equatorial Waves with Critical Latitude" with Andrei Natarov, submitted to Appl. Math. Comput. (1999).
119. "Additive blending of local approximations into a globally-valid approximation with application to new analytic approximations to the dilogarithm", submitted to Appl. Math. Lett., (1999).
120. "Stability and Long-Time Evolution of the Periodic Solutions to the Two Coupled Nonlinear Schroedinger Equations", with Benkui Tan, submitted to Chaos, Fractals and Solitons (1999).
121. "Weakly nonlinear wavepackets in the Korteweg-deVries equation: The KdV/NLS connection", with Guan-yu Chen, submitted to Math. Comput. Simulation, (1999).