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:
email: 
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 AfricanAmerican 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 coauthor Abba Gumel at CAARMS9
RESEARCH NOTES
From 1968 to 1999, Dr. Mickens published 5
books and 170 papers.
SELECTED PUBLICATIONS
Books by Ronald Mickens
 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: 9810222920
 Mickens, Ronald E. Nonstandard finite difference models
of differential equations, World Scientific Publishing Co.,
Inc., River Edge, NJ, 1994. xii+249 pp. ISBN: 9810214588
 Mickens, Ronald E. Difference equations. Theory and
applications. Second edition. Van Nostrand Reinhold Co., New
York, 1990. xii+448 pp. ISBN: 0442001363
 Mickens, Ronald E. Difference equations, Van Nostrand
Reinhold Co., New YorkLondon, 1987. xii+243 pp. ISBN: 0442260768
 Mickens, Ronald E. Mathematical analysis of physical systems,
Van Nostrand Reinhold Co., New YorkLondon, 1985, x+357 pp. ISBN:
0442260776
 Mickens, Ronald E. An introduction to nonlinear oscillations,
Cambridge University Press, CambridgeNew York, 1981. xiv+224
pp. ISBN: 0521222087
 Mathematics and science. Edited by Ronald E. Mickens.
World Scientific Publishing Co., Inc., Teaneck, NJ, 1990. x+342
pp. ISBN: 9810202334
selected papers by Ronald Elbert
Mickens
 R.E. Mickens and A.B.
Gumel. Numerical study of a nonstandard finitedifference
scheme for the van der Pol equation. Journal of Sound and
Vibration. 250(5)(2002): 955963.
 Mickens, R. E. Periodic solutions of the relativistic
harmonic oscillator. J. Sound Vibration 212
(1998), no. 5, 905908.
 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, 790793.
 Mickens, Ronald E. A finite difference scheme for
traveling wave solutions to Burgers equation. Numer.
Methods Partial Differential Equations 14 (1998), no.
6, 815820.
 Mickens, Ronald E.; Brewley, Denise N.; Russell, Matasha
L. A model of dieting. SIAM Rev. 40, No.3,
667672 (1998).
 Mickens, R.E. Nonstandard finite difference scheme
for a scalar reactionconvection PDE. J. Difference
Equ. Appl. 3, No.56, 359367 (1998).
 Mickens, R.E. Asymptotic properties of solutions
to two discrete Airy equations. J. Difference Equ.
Appl. 3, No.34, 231239 (1998).
 Mickens, Ronald E. Relation between the time and
space stepsizes in nonstandard finitedifference schemes for
the Fisher equation. Numer. Methods Partial Differential
Equations 13 (1997), no. 1, 5155. 65M06
 R.E. Mickens and 'Kale
Oyedeji, International Journal of Applied Science and
Computations, 4,1, 99 (June 1997), ed. S.K. Dey.
 Mickens, Ronald E. Relation between the time and
space stepsizes for Fisher partial differential equation,
Internat. J. Appl. Sci. Comput. 2 (1996), 423424. 65M99
 Mickens, R. E. Exact finite difference schemes
for the wave equation with spherical symmetry. J. Differ.
Equations Appl. 2 (1996), no. 3, 263269.
 Mickens, R. E. Comments on the Shohat expansion.
J. Sound Vibration 193 (1996), no. 3, 747749.
 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 1214, 1995); pp 9195.
 Mickens, Ronald E. Nonstandard finite difference
models of differential equations, World Scientific
Publishing Co., Inc., River Edge, NJ, 249 (1994), 65102
 R.E. Mickens and O.
Oyedeji, J. Sound and Vibration, 178, 285 (1994)
 Mickens, Ronald E. A new finitedifference scheme
for Schrödinger type partial differential equations,
Computational acoustics, Vol. 2 (1993), 233239.
 Mickens, Ronald E. Calculation of oscillatory properties
of the solutions of two coupled, first order nonlinear ordinary
differential equations, J. Sound Vibration 137 (1990),
331334.
 Mickens, Ronald E. Investigation of finitedifference
models of the van der Pol equation, Differential equations
and applications, Vol. I, II (1989), 210215.
 Mickens, Ronald E. Mathematical properties of the
vacuum polarization function , Lett. Math. Phys. 2
(1977/78), 343347
 Mickens, Ronald E. Bounds on the phase of the forward
scattering amplitude and the Pomeranchuk theorem , Lett.
Nuovo Cimento 3 (1970 ), 428432
 Burnette, J. E.; Mickens, R. E. Spurious limitcycles
arising in higher order averaging methods. J. Sound Vibration
193 (1996), no. 3, 743746.
 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, 185193.
 Mickens, R. E. Construction of asymptotic solutions
to discrete Bessel equations. Advances in difference equations.
Comput. Math. Appl. 28 (1994), no. 13, 219226.
 Nageswara Rao, B. Comments on: "Harmonic balance: comparison
of equation of motion and energy methods" [J. Sound Vibration
{\bf 164} (1993), no. 1, 179181; MR 94h:34046] by S. Hiamang
and R. E. Mickens. With a reply by Mickens. J.
Sound Vibration 172 (1994), no. 5, 697699.
 Mickens, Ronald E. A best finitedifference scheme
for the Fisher equation. Numer. Methods Partial Differential
Equations 10 (1994), no. 5, 581585.
 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, 564567.
 Hiamang, S.; Mickens, R. E. Harmonic balance: comparison
of equation of motion and energy methods. J. Sound Vibration
164 (1993), no. 1, 179181.
 Mickens, R. E.; Mixon, M. Application of generalized
harmonic balance to an antisymmetric quadratic nonlinear oscillator.
J. Sound Vibration 159 (1992), no. 3, 546548.
 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,
180182.
 Mickens, Ronald E. Novel explicit finitedifference
schemes for timedependent Schrödinger equations. Comput.
Phys. Comm. 63 (1991), no. 13, 203208.
 Mickens, R. E.; Shoosmith, J. N. A discrete model
of a modified Burgers' partial differential equation. J.
Sound Vibration 142 (1990), no. 3, 536539.
 Mickens, R. E. Calculation of transient behavior
for a nonlinear, singular oscillator equation. J. Sound Vibration
134 (1989), no. 1, 187189.
 Mickens, Ronald E. Investigation of the mathematical
properties of a new negative resistance oscillator model.
Circuits Systems Signal Process. 8 (1989), no. 2, 187205.
 Mickens, R. E. Construction of a perturbation solution
for a nonlinear, singular oscillator equation. J. Sound Vibration
130 (1989), no. 3, 513515.
 Mickens, Ronald E. Exact solutions to a population
model: the logistic equation with advection. SIAM Rev. 30
(1988), no. 4, 629633.
 Mickens, Ronald E. Stable explicit schemes for
equations of Schrödinger type. Phys. Rev. A (3) 39
(1989), no. 11, 55085511.
 Mickens, R. E. Perturbation procedure for the van
der Pol oscillator based on the Hopf bifurcation theorem.
J. Sound Vibration 127 (1988), no. 1, 187191.
 Mickens, Ronald E. Difference equation models of
differential equations. Mathematical modelling in science
and technology (St. Louis, MO, 1987). Math. Comput. Modelling
11 (1988), 528530.
 Mickens, R. E. Properties of finite difference
models of nonlinear conservative oscillators. J. Sound Vibration
124 (1988), no. 1, 194198.
 Mickens, Ronald E. RungeKutta schemes and numerical
instabilities: the logistic equation. Differential equations
and mathematical physics (Birmingham, Ala., 1986), 337341,
Lecture Notes in Math., 1285, Springer, BerlinNew York,
1987.
 Mickens, R. E. Bounds on the Fourier coefficients
for the periodic solutions of nonlinear oscillator equations.
J. Sound Vibration 124 (1988), no. 1, 199203.
 Mickens, R. E. Iteration procedure for determining
approximate solutions to nonlinear oscillator equations.
J. Sound Vibration 116 (1987), no. 1, 185187.
 Mickens, Ronald E. Mathematical modeling of differential
equations by difference equations. Computational acoustics,
Vol. I (New Haven, Conn., 1986), 387393, NorthHolland, AmsterdamNew
York, 1988.
 Mickens, Ronald E. Periodic solutions of secondorder
nonlinear difference equations containing a small parameter.
IV. Multidiscrete time method. J. Franklin Inst. 324 (1987),
no. 2, 263271.
 Mickens, Ronald E. Singular nonlinear oscillator
equations. Nonlinear analysis and applications (Arlington,
Tex., 1986), 339344, Lecture Notes in Pure and Appl. Math.,
109, Dekker, New York, 1987.
 Mickens, R. E. Analysis of the damped pendulum.
J. Sound Vibration 115 (1987), no. 2, 374378.
 Mickens, Ronald E. Singular nonlinear oscillations:
method of harmonic balance. Complex and distributed systems
(Oslo, 1985), 157161, IMACS Trans. Sci. Comput.85,
IV, NorthHolland, AmsterdamNew York, 1986.
 Mickens, R. E. A generalization of the method of
harmonic balance. J. Sound Vibration 111 (1986), no.
3, 515518.
 Mickens, Ronald E. Exact solutions to difference
equation models of Burgers' equation. Numer. Methods Partial
Differential Equations 2 (1986), no. 2, 123129.
 Mickens, R. E.; Semwogerere,
D. Fourier analysis of a rational harmonic balance
approximation for periodic solutions. J. Sound Vibration
195 (1996), no. 3, 528530. 34C25 [53] 1 389 343
 Mickens, Ronald E.; Ramadhani, Issa WKB procedure
for Schrödinger type difference equations. World Congress
of Nonlinear Analysts '92, Vol. IIV (Tampa, FL, 1992), 39073912,
de Gruyter, Berlin, 1996.
 Mickens, Ronald E. Relation between the time and
space stepsizes for Fisher partial differential equation.
Internat. J. Appl. Sci. Comput. 2 (1996), no. 3, 423424.
 Mickens, Ronald E. Mathematical properties of a
nonlinear finitedifference scheme for the linear timedependent
Schrödinger equation. Neural, parallel and scientific
computations, Vol. 1 (Atlanta, GA, 1995), 333339, Dynamic,
Atlanta, GA, 1995.
 AddoAsah, W.; Akpati, H. C.; Mickens, R. E. Investigation
of a generalized van der Pol oscillator differential equation.
J. Sound Vibration 179 (1995), no. 4, 733735.
 Mickens, Ronald E. Relations between the time and
space stepsizes for finitedifference models of PDEs. J.
Appl. Sci. Comput. 1 (1995), no. 3, 520527.
 Mickens, Ronald E. Genesis of elementary numerical
instabilities in finitedifference models of ordinary differential
equations. Proceedings of Dynamic Systems and Applications,
Vol. 1 (Atlanta, GA, 1993), 251257, Dynamic, Atlanta, GA, 1994.
 Mickens, Ronald E. Comment on: "A secondorder,
chaosfree, explicit method for the numerical solution of a cubic
reaction problem in neurophysiology" [Numer.\ Methods Partial
Differential Equations 9 (1993), no. 3, 213224; by W.
G. Price, Y. Wang and E. H. Twizell. Numer. Methods Partial Differential
Equations 10 (1994), no. 5, 587590.
 Mickens, R. E. Construction of a finitedifference
scheme that exactly conserves energy for a mixed parity oscillator.
J. Sound Vibration 172 (1994), no. 1, 142144.
 Mickens, R. E.; Ramadhani, I. Finitedifference
schemes having the correct linear stability properties for all
finite stepsizes. III. Comput. Math. Appl. 27 (1994),
no. 4, 7784.
 Lipscomb, T.; Mickens, R. E. Exact solution to
the antisymmetric, constant force oscillator equation. J.
Sound Vibration 169 (1994), no. 1, 138140.
 Mickens, Ronald E. A new finitedifference scheme
for Schrödinger type partial differential equations.
Computational acoustics, Vol. 2 (Cambridge, MA, 1991),
233239, NorthHolland, Amsterdam, 1993.
 Mickens, R. E. Finitedifference schemes having
the correct linear stability properties for all finite stepsizes.
Ordinary and delay differential equations (Edinburg, TX, 1991),
139143, Pitman Res. Notes Math. Ser., 272, Longman Sci.
Tech., Harlow, 1992.
 Mickens, Ronald E. Finitedifference schemes having
the correct linear stability properties for all finite stepsizes.
II. Dynam. Systems Appl. 1 (1992), no. 3, 329340.
 Mickens, R. E.; Ramadhani, I. Investigation of
an antisymmetric quadratic nonlinear oscillator. J. Sound
Vibration 155 (1992), no. 1, 190193.
 Mickens, R. E.; Oyedeji, O. Dual periodic modes
for two linearly coupled identical singular oscillators.
J. Sound Vibration 153 (1992), no. 3, 548551.
 Mickens, Ronald E. Construction of a novel finitedifference
scheme for a nonlinear diffusion equation. Numer. Methods
Partial Differential Equations 7 (1991), no. 3, 299302.
 Mickens, R. E. Analysis of a new finitedifference
scheme for the linear advectiondiffusion equation. J. Sound
Vibration 146 (1991), no. 2, 342344.
 Mickens, R. E.; Bota, K. Periodic symmetry modes
of two coupled identical singular oscillators. J. Sound Vibration
143 (1990), no. 1, 180181.
 Mickens, Ronald E. Construction of stable explicit
finitedifference schemes for Schrödinger type differential
equations. Computational acoustics, Vol. 1 (Princeton,
NJ, 1989), 1116, NorthHolland, Amsterdam, 1990.
 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, 331334.
 Collins, W. E.; Mickens, R. E. Symmetry properties
of van der Pol type differential equations and implications.
J. Sound Vibration 136 (1990), no. 2, 352354.
 Mickens, Ronald E.; Smith, Arthur Finitedifference
models of ordinary differential equations: influence of denominator
functions. J. Franklin Inst. 327 (1990), no. 1, 143149.
 Mickens, Ronald E. Exact solutions to a finitedifference
model of a nonlinear reactionadvection equation: implications
for numerical analysis. Numer. Methods Partial Differential
Equations 5 (1989), no. 4, 313325.
 Mickens, Ronald E. Investigation of finitedifference
models of the van der Pol equation. Differential equations
and applications, Vol. I, II (Columbus, OH, 1988), 210215,
Ohio Univ. Press, Athens, OH, 1989.
 Mickens, Ronald E. Periodic solutions of secondorder
nonlinear difference equations containing a small parameter.
III. Perturbation theory. J. Franklin Inst. 321 (1986),
no. 1, 3947.
 Mickens, Ronald E. Periodic solutions of secondorder
nonlinear difference equations containing a small parameter.
II. Equivalent linearization. J. Franklin Inst. 320
(1985), no. 34, 169174.
 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, 579582.
 Mickens, R. E. Exact finite difference schemes
for the nonlinear unidirectional wave equation. J. Sound
Vibration 100 (1985), no. 3, 452455.
 WigginsGrandison, M. D.; Mickens, R. E. Exact
solutions of nonlinear unidirectional wave equations. J.
Sound Vibration 97 (1984), no. 1, 165167.
 Mickens, Ronald E. Difference equation models of
differential equations having zero local truncation errors.
Differential equations (Birmingham, Ala., 1983), 445449, NorthHolland
Math. Stud., 92, NorthHolland, AmsterdamNew York, 1984.
 Mickens, Ronald E. Periodic solutions of secondorder
nonlinear difference equations containing a small parameter.
J. Franklin Inst. 316 (1983), no. 3, 273277.
 Mickens, R. E. A regular perturbation technique
for nonlinearly coupled oscillators in resonance. J. Sound
Vibration 81 (1982), no. 2, 307310.
 Mickens, Ronald E. Mathematical properties of the
vacuum polarization function. Lett. Math. Phys. 2
(1977/78), no. 5, 343347.
 Mickens, R. E. Bounds on the phase of the forward
scattering amplitude and the Pomeranchuk theorem. Lett. Nuovo
Cimento 3 1970 428432.
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