Ronald E. Mickens

Born February 7, 1943

Birthplace:: Petersburg, Virginia

Area of Research Interests: Mathematical Physics

B.S. (1964) Mathematics and Physics Fisk University

Ph.D. (1968) Theoretical Physics Vanderbilt University

: Professor of Physics Atlanta University
URL:
e-mail:

In 1964, Ronald Elbert Mickens graduated with a B.S. in mathematics and physics from Fisk University in Nashville, Tennessee and enrolled as a graduate student in Physics at Vanderbilt University with Wodrow Wilson and Danforth Scholarships. Mickens earned a Ph.D. in Theoretical Physics from Vanderbilt im 1968. From 1968 to 1970, Dr. Mickens had a postdoctoral position at M.I.T.

In 1970, Dr. Ronald E. Mickens was appointed a professor of Physics at Fisk University where he remained until 1982 when he became a Professor of Physics at Clark Atlanta Universty. In 1985 Dr. Mickens was named Callaway Professor of Physics at Clark Atlanta. His research is in Mathematics and Physics.

In addition to research, his efforts to open Physics to Blacks are very important and he serves as Historian for the National Society of Black Physicists. Recently, Mickens was honored with an election to Fellowship in the American Physical Society, a rare position limited to .5% of the membership of the society. In 1999, Mickens personally published a history book: The African American Presence in Physics, and has just published (2002) the book Edward Bouchet, The First African-American Doctorate.
Dr. Mickens mailing address is

Clark Atlanta University
Box 172 - Physics Department
Atlanta, Georgia 30314

Also see the web page: Who are the greatest Black Mathematicians?

 

references: Mathematical Reviews, [nba99 pg229]


Ron Mickens with co-author Abba Gumel at CAARMS9

RESEARCH NOTES

From 1968 to 1999, Dr. Mickens published 5 books and 170 papers.

SELECTED PUBLICATIONS

Books by Ronald Mickens

  1. Mickens, Ronald E. Oscillations in planar dynamic systems, Series on Advances in Mathematics for Applied Sciences, 37. World Scientific Publishing Co., Inc., River Edge, NJ, 1996. xiv+319 pp. ISBN: 981-02-2292-0
  2. Mickens, Ronald E. Nonstandard finite difference models of differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. xii+249 pp. ISBN: 981-02-1458-8
  3. Mickens, Ronald E. Difference equations. Theory and applications. Second edition. Van Nostrand Reinhold Co., New York, 1990. xii+448 pp. ISBN: 0-442-00136-3
  4. Mickens, Ronald E. Difference equations, Van Nostrand Reinhold Co., New York-London, 1987. xii+243 pp. ISBN: 0-442-26076-8
  5. Mickens, Ronald E. Mathematical analysis of physical systems, Van Nostrand Reinhold Co., New York-London, 1985, x+357 pp. ISBN: 0-442-26077-6
  6. Mickens, Ronald E. An introduction to nonlinear oscillations, Cambridge University Press, Cambridge-New York, 1981. xiv+224 pp. ISBN: 0-521-22208-7
  7. Mathematics and science. Edited by Ronald E. Mickens. World Scientific Publishing Co., Inc., Teaneck, NJ, 1990. x+342 pp. ISBN: 981-02-0233-4

selected papers by Ronald Elbert Mickens

  1. R.E. Mickens and A.B. Gumel. Numerical study of a nonstandard finite-difference scheme for the van der Pol equation. Journal of Sound and Vibration. 250(5)(2002): 955-963.
  2. Mickens, R. E. Periodic solutions of the relativistic harmonic oscillator. J. Sound Vibration 212 (1998), no. 5, 905--908.
  3. Mickens, Ronald E. Liénard systems, limit cycles, Melnikov theory, and the method of slowly varying amplitude and phase. J. Sound Vibration 217 (1998), no. 4, 790--793.
  4. Mickens, Ronald E. A finite difference scheme for traveling wave solutions to Burgers equation. Numer. Methods Partial Differential Equations 14 (1998), no. 6, 815--820.
  5. Mickens, Ronald E.; Brewley, Denise N.; Russell, Matasha L. A model of dieting. SIAM Rev. 40, No.3, 667-672 (1998).
  6. Mickens, R.E. Nonstandard finite difference scheme for a scalar reaction-convection PDE. J. Difference Equ. Appl. 3, No.5-6, 359-367 (1998).
  7. Mickens, R.E. Asymptotic properties of solutions to two discrete Airy equations. J. Difference Equ. Appl. 3, No.3-4, 231-239 (1998).
  8. Mickens, Ronald E. Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation. Numer. Methods Partial Differential Equations 13 (1997), no. 1, 51--55. 65M06
  9. R.E. Mickens and 'Kale Oyedeji, International Journal of Applied Science and Computations, 4,1, 99 (June 1997), ed. S.K. Dey.
  10. Mickens, Ronald E. Relation between the time and space step-sizes for Fisher partial differential equation, Internat. J. Appl. Sci. Comput. 2 (1996), 423--424. 65M99
  11. Mickens, R. E. Exact finite difference schemes for the wave equation with spherical symmetry. J. Differ. Equations Appl. 2 (1996), no. 3, 263--269.
  12. Mickens, R. E. Comments on the Shohat expansion. J. Sound Vibration 193 (1996), no. 3, 747--749.
  13. R.E. Mickens and Oyekale Oyedeji, "Numerical Stabilities: The details matter." Proceedings of Advances in Scientific Computing and Modeling (eds. S.K. Dey and J. Ziebarth; Eastern Illinois University, Charleston, IL; October 12-14, 1995); pp 91-95.
  14. Mickens, Ronald E. Nonstandard finite difference models of differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 249 (1994), 65-102
  15. R.E. Mickens and O. Oyedeji, J. Sound and Vibration, 178, 285 (1994)
  16. Mickens, Ronald E. A new finite-difference scheme for Schrödinger type partial differential equations, Computational acoustics, Vol. 2 (1993), 233--239.
  17. Mickens, Ronald E. Calculation of oscillatory properties of the solutions of two coupled, first order nonlinear ordinary differential equations, J. Sound Vibration 137 (1990), 331--334.
  18. Mickens, Ronald E. Investigation of finite-difference models of the van der Pol equation, Differential equations and applications, Vol. I, II (1989), 210--215.
  19. Mickens, Ronald E. Mathematical properties of the vacuum polarization function , Lett. Math. Phys. 2 (1977/78), 343-347
  20. Mickens, Ronald E. Bounds on the phase of the forward scattering amplitude and the Pomeranchuk theorem , Lett. Nuovo Cimento 3 (1970 ), 428-432
  21. Burnette, J. E.; Mickens, R. E. Spurious limit-cycles arising in higher order averaging methods. J. Sound Vibration 193 (1996), no. 3, 743--746.
  22. Mickens, Ronald E. Construction of finite difference schemes for coupled nonlinear oscillators derived from a discrete energy function. Difference equations: theory and applications (San Francisco, CA, 1995). J. Differ. Equations Appl. 2 (1996), no. 2, 185--193.
  23. Mickens, R. E. Construction of asymptotic solutions to discrete Bessel equations. Advances in difference equations. Comput. Math. Appl. 28 (1994), no. 1-3, 219--226.
  24. Nageswara Rao, B. Comments on: "Harmonic balance: comparison of equation of motion and energy methods" [J. Sound Vibration {\bf 164} (1993), no. 1, 179--181; MR 94h:34046] by S. Hiamang and R. E. Mickens. With a reply by Mickens. J. Sound Vibration 172 (1994), no. 5, 697--699.
  25. Mickens, Ronald E. A best finite-difference scheme for the Fisher equation. Numer. Methods Partial Differential Equations 10 (1994), no. 5, 581--585.
  26. Mickens, R. E. Construction of a perturbation solution to a mixed parity system that satisfies the correct initial conditions. J. Sound Vibration 167 (1993), no. 3, 564--567.
  27. Hiamang, S.; Mickens, R. E. Harmonic balance: comparison of equation of motion and energy methods. J. Sound Vibration 164 (1993), no. 1, 179--181.
  28. Mickens, R. E.; Mixon, M. Application of generalized harmonic balance to an anti-symmetric quadratic nonlinear oscillator. J. Sound Vibration 159 (1992), no. 3, 546--548.
  29. Mickens, R. E.; Ramadhani, I. Failure of the method of slowly varying amplitude and phase for nonlinear, singular oscillators. J. Sound Vibration 152 (1992), no. 1, 180--182.
  30. Mickens, Ronald E. Novel explicit finite-difference schemes for time-dependent Schrödinger equations. Comput. Phys. Comm. 63 (1991), no. 1-3, 203--208.
  31. Mickens, R. E.; Shoosmith, J. N. A discrete model of a modified Burgers' partial differential equation. J. Sound Vibration 142 (1990), no. 3, 536--539.
  32. Mickens, R. E. Calculation of transient behavior for a nonlinear, singular oscillator equation. J. Sound Vibration 134 (1989), no. 1, 187--189.
  33. Mickens, Ronald E. Investigation of the mathematical properties of a new negative resistance oscillator model. Circuits Systems Signal Process. 8 (1989), no. 2, 187--205.
  34. Mickens, R. E. Construction of a perturbation solution for a nonlinear, singular oscillator equation. J. Sound Vibration 130 (1989), no. 3, 513--515.
  35. Mickens, Ronald E. Exact solutions to a population model: the logistic equation with advection. SIAM Rev. 30 (1988), no. 4, 629--633.
  36. Mickens, Ronald E. Stable explicit schemes for equations of Schrödinger type. Phys. Rev. A (3) 39 (1989), no. 11, 5508--5511.
  37. Mickens, R. E. Perturbation procedure for the van der Pol oscillator based on the Hopf bifurcation theorem. J. Sound Vibration 127 (1988), no. 1, 187--191.
  38. Mickens, Ronald E. Difference equation models of differential equations. Mathematical modelling in science and technology (St. Louis, MO, 1987). Math. Comput. Modelling 11 (1988), 528--530.
  39. Mickens, R. E. Properties of finite difference models of nonlinear conservative oscillators. J. Sound Vibration 124 (1988), no. 1, 194--198.
  40. Mickens, Ronald E. Runge-Kutta schemes and numerical instabilities: the logistic equation. Differential equations and mathematical physics (Birmingham, Ala., 1986), 337--341, Lecture Notes in Math., 1285, Springer, Berlin-New York, 1987.
  41. Mickens, R. E. Bounds on the Fourier coefficients for the periodic solutions of nonlinear oscillator equations. J. Sound Vibration 124 (1988), no. 1, 199--203.
  42. Mickens, R. E. Iteration procedure for determining approximate solutions to nonlinear oscillator equations. J. Sound Vibration 116 (1987), no. 1, 185--187.
  43. Mickens, Ronald E. Mathematical modeling of differential equations by difference equations. Computational acoustics, Vol. I (New Haven, Conn., 1986), 387--393, North-Holland, Amsterdam-New York, 1988.
  44. Mickens, Ronald E. Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV. Multidiscrete time method. J. Franklin Inst. 324 (1987), no. 2, 263--271.
  45. Mickens, Ronald E. Singular nonlinear oscillator equations. Nonlinear analysis and applications (Arlington, Tex., 1986), 339--344, Lecture Notes in Pure and Appl. Math., 109, Dekker, New York, 1987.
  46. Mickens, R. E. Analysis of the damped pendulum. J. Sound Vibration 115 (1987), no. 2, 374--378.
  47. Mickens, Ronald E. Singular nonlinear oscillations: method of harmonic balance. Complex and distributed systems (Oslo, 1985), 157--161, IMACS Trans. Sci. Comput.---85, IV, North-Holland, Amsterdam-New York, 1986.
  48. Mickens, R. E. A generalization of the method of harmonic balance. J. Sound Vibration 111 (1986), no. 3, 515--518.
  49. Mickens, Ronald E. Exact solutions to difference equation models of Burgers' equation. Numer. Methods Partial Differential Equations 2 (1986), no. 2, 123--129.
  50. Mickens, R. E.; Semwogerere, D. Fourier analysis of a rational harmonic balance approximation for periodic solutions. J. Sound Vibration 195 (1996), no. 3, 528--530. 34C25 [53] 1 389 343
  51. Mickens, Ronald E.; Ramadhani, Issa WKB procedure for Schrödinger type difference equations. World Congress of Nonlinear Analysts '92, Vol. I--IV (Tampa, FL, 1992), 3907--3912, de Gruyter, Berlin, 1996.
  52. Mickens, Ronald E. Relation between the time and space step-sizes for Fisher partial differential equation. Internat. J. Appl. Sci. Comput. 2 (1996), no. 3, 423--424.
  53. Mickens, Ronald E. Mathematical properties of a nonlinear finite-difference scheme for the linear time-dependent Schrödinger equation. Neural, parallel and scientific computations, Vol. 1 (Atlanta, GA, 1995), 333--339, Dynamic, Atlanta, GA, 1995.
  54. Addo-Asah, W.; Akpati, H. C.; Mickens, R. E. Investigation of a generalized van der Pol oscillator differential equation. J. Sound Vibration 179 (1995), no. 4, 733--735.
  55. Mickens, Ronald E. Relations between the time and space step-sizes for finite-difference models of PDEs. J. Appl. Sci. Comput. 1 (1995), no. 3, 520--527.
  56. Mickens, Ronald E. Genesis of elementary numerical instabilities in finite-difference models of ordinary differential equations. Proceedings of Dynamic Systems and Applications, Vol. 1 (Atlanta, GA, 1993), 251--257, Dynamic, Atlanta, GA, 1994.
  57. Mickens, Ronald E. Comment on: "A second-order, chaos-free, explicit method for the numerical solution of a cubic reaction problem in neurophysiology" [Numer.\ Methods Partial Differential Equations 9 (1993), no. 3, 213--224; by W. G. Price, Y. Wang and E. H. Twizell. Numer. Methods Partial Differential Equations 10 (1994), no. 5, 587--590.
  58. Mickens, R. E. Construction of a finite-difference scheme that exactly conserves energy for a mixed parity oscillator. J. Sound Vibration 172 (1994), no. 1, 142--144.
  59. Mickens, R. E.; Ramadhani, I. Finite-difference schemes having the correct linear stability properties for all finite step-sizes. III. Comput. Math. Appl. 27 (1994), no. 4, 77--84.
  60. Lipscomb, T.; Mickens, R. E. Exact solution to the antisymmetric, constant force oscillator equation. J. Sound Vibration 169 (1994), no. 1, 138--140.
  61. Mickens, Ronald E. A new finite-difference scheme for Schrödinger type partial differential equations. Computational acoustics, Vol. 2 (Cambridge, MA, 1991), 233--239, North-Holland, Amsterdam, 1993.
  62. Mickens, R. E. Finite-difference schemes having the correct linear stability properties for all finite step-sizes. Ordinary and delay differential equations (Edinburg, TX, 1991), 139--143, Pitman Res. Notes Math. Ser., 272, Longman Sci. Tech., Harlow, 1992.
  63. Mickens, Ronald E. Finite-difference schemes having the correct linear stability properties for all finite step-sizes. II. Dynam. Systems Appl. 1 (1992), no. 3, 329--340.
  64. Mickens, R. E.; Ramadhani, I. Investigation of an anti-symmetric quadratic nonlinear oscillator. J. Sound Vibration 155 (1992), no. 1, 190--193.
  65. Mickens, R. E.; Oyedeji, O. Dual periodic modes for two linearly coupled identical singular oscillators. J. Sound Vibration 153 (1992), no. 3, 548--551.
  66. Mickens, Ronald E. Construction of a novel finite-difference scheme for a nonlinear diffusion equation. Numer. Methods Partial Differential Equations 7 (1991), no. 3, 299--302.
  67. Mickens, R. E. Analysis of a new finite-difference scheme for the linear advection-diffusion equation. J. Sound Vibration 146 (1991), no. 2, 342--344.
  68. Mickens, R. E.; Bota, K. Periodic symmetry modes of two coupled identical singular oscillators. J. Sound Vibration 143 (1990), no. 1, 180--181.
  69. Mickens, Ronald E. Construction of stable explicit finite-difference schemes for Schrödinger type differential equations. Computational acoustics, Vol. 1 (Princeton, NJ, 1989), 11--16, North-Holland, Amsterdam, 1990.
  70. Mickens, R. E. Calculation of oscillatory properties of the solutions of two coupled, first order nonlinear ordinary differential equations. J. Sound Vibration 137 (1990), no. 2, 331--334.
  71. Collins, W. E.; Mickens, R. E. Symmetry properties of van der Pol type differential equations and implications. J. Sound Vibration 136 (1990), no. 2, 352--354.
  72. Mickens, Ronald E.; Smith, Arthur Finite-difference models of ordinary differential equations: influence of denominator functions. J. Franklin Inst. 327 (1990), no. 1, 143--149.
  73. Mickens, Ronald E. Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: implications for numerical analysis. Numer. Methods Partial Differential Equations 5 (1989), no. 4, 313--325.
  74. Mickens, Ronald E. Investigation of finite-difference models of the van der Pol equation. Differential equations and applications, Vol. I, II (Columbus, OH, 1988), 210--215, Ohio Univ. Press, Athens, OH, 1989.
  75. Mickens, Ronald E. Periodic solutions of second-order nonlinear difference equations containing a small parameter. III. Perturbation theory. J. Franklin Inst. 321 (1986), no. 1, 39--47.
  76. Mickens, Ronald E. Periodic solutions of second-order nonlinear difference equations containing a small parameter. II. Equivalent linearization. J. Franklin Inst. 320 (1985), no. 3-4, 169--174.
  77. Mickens, R. E.; Oyedeji, K. Construction of approximate analytical solutions to a new class of nonlinear oscillator equation. J. Sound Vibration 102 (1985), no. 4, 579--582.
  78. Mickens, R. E. Exact finite difference schemes for the nonlinear unidirectional wave equation. J. Sound Vibration 100 (1985), no. 3, 452--455.
  79. Wiggins-Grandison, M. D.; Mickens, R. E. Exact solutions of nonlinear unidirectional wave equations. J. Sound Vibration 97 (1984), no. 1, 165--167.
  80. Mickens, Ronald E. Difference equation models of differential equations having zero local truncation errors. Differential equations (Birmingham, Ala., 1983), 445--449, North-Holland Math. Stud., 92, North-Holland, Amsterdam-New York, 1984.
  81. Mickens, Ronald E. Periodic solutions of second-order nonlinear difference equations containing a small parameter. J. Franklin Inst. 316 (1983), no. 3, 273--277.
  82. Mickens, R. E. A regular perturbation technique for nonlinearly coupled oscillators in resonance. J. Sound Vibration 81 (1982), no. 2, 307--310.
  83. Mickens, Ronald E. Mathematical properties of the vacuum polarization function. Lett. Math. Phys. 2 (1977/78), no. 5, 343--347.
  84. Mickens, R. E. Bounds on the phase of the forward scattering amplitude and the Pomeranchuk theorem. Lett. Nuovo Cimento 3 1970 428--432.

 

The web pages
MATHEMATICIANS OF THE AFRICAN DIASPORA
are brought to you by

The Mathematics Department of
The State University of New York at Buffalo.

They are created and maintained by
Scott W. Williams
Professor of Mathematics

CONTACT Dr. Williams