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## Mickens, Ronald Elbert

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 Author ID: mickens.ronald-e Published as: Mickens, E. R.; Mickens, R. E.; Mickens, Ronald; Mickens, Ronald E. External Links: Wikidata · GND
 Documents Indexed: 215 Publications since 1980, including 13 Books Biographic References: 3 Publications
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#### Co-Authors

 138 single-authored 9 Oyedeji, Kale 9 Rucker, Sandra A. 6 Gumel, Abba B. 6 Jordan, Pedro M. 5 Washington, Talitha Michal 4 Ehrhardt, Matthias 3 Chapwanya, Michael 3 Dai, Weizhong 3 Lubuma, Jean Mbaro-Saman 3 Ramadhani, Issa 3 Roeger, Lih-Ing Wu 2 Burnette, J. E. 2 Clemence, Dominic P. 2 Kovacic, Ivana 2 Oyedeji, O. 2 Semwogerere, Denis 2 Serfaty de Markus, Alicia 2 Wilkerson, Dorian 1 Addo-Asah, W. 1 Adeyemi, Hezekiah O. 1 Akpati, H. C. 1 Beatty, John C. 1 Bejan, Adrian 1 Bellamy, Michael 1 Bota, K. 1 Brewley, Denise N. 1 Buckmire, Ron 1 Caguiat, Jonathan J. 1 Castillo-Chavez, Carlos 1 Chen, Zikang 1 Collins, W. E. 1 Cooper, Keith D. 1 Corbett, B. D. 1 Divens, Garrett 1 George, Roy 1 Harrison, Scott H. 1 Herring, Patricia A. 1 Herron, Isom H. jun. 1 Holmes, Raquelle 1 Jackson, D. D. 1 Jackson, Julius H. 1 Letellier, Christophe 1 Lewis, Torina 1 Lipscomb, Tyson 1 Liu, Liping 1 McCalla, Clement 1 Mcintyre, C. R. 1 McMurtry, Karl 1 Mendes, Eduardo M. A. M. 1 Mixon, M. 1 Moghadas, Seyed M. 1 Mulks, Charles F. 1 Munyakazi, Justin B. 1 Pleasant, James C. 1 Russell, Matasha L. 1 Shoosmith, John N. 1 Simpson, Carlos Tschudi 1 Smith, Arthur L. 1 Speight, K. R. 1 Srikanth, Radhakrishnan 1 Su, Shaojing 1 Wang, Haojie 1 Winrow, Michael A.
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#### Serials

 65 Journal of Sound and Vibration 32 Journal of Difference Equations and Applications 17 Numerical Methods for Partial Differential Equations 8 Computers & Mathematics with Applications 6 Mathematics and Computers in Simulation 5 Journal of the Franklin Institute 3 Journal of Computational and Applied Mathematics 3 Discrete and Continuous Dynamical Systems 3 Series on Advances in Mathematics for Applied Sciences 3 Journal of Biological Dynamics 2 International Journal of Heat and Mass Transfer 2 Mechanics Research Communications 2 Mathematical and Computer Modelling 2 SIAM Review 2 Neural, Parallel & Scientific Computations 2 Journal of Computational Methods in Sciences and Engineering 1 Computer Physics Communications 1 Mathematical Biosciences 1 Applied Mathematics and Computation 1 Circuits, Systems, and Signal Processing 1 Applied Numerical Mathematics 1 Applied Mathematics Letters 1 Dynamic Systems and Applications 1 Notices of the American Mathematical Society 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Mathematical Modelling and Scientific Computing 1 Nonlinear Dynamics 1 International Journal of Theoretical and Applied Finance 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Biological Systems 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Journal of Computational Acoustics 1 Contemporary Mathematics 1 The College Mathematics Journal 1 Advances in Applied Mathematics and Mechanics 1 Evolution Equations and Control Theory 1 Monographs and Research Notes in Mathematics
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#### Fields

 109 Ordinary differential equations (34-XX) 104 Numerical analysis (65-XX) 52 Partial differential equations (35-XX) 37 Mechanics of particles and systems (70-XX) 32 Biology and other natural sciences (92-XX) 29 Difference and functional equations (39-XX) 10 Special functions (33-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 General and overarching topics; collections (00-XX) 6 Fluid mechanics (76-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Mechanics of deformable solids (74-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Quantum theory (81-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Systems theory; control (93-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH

161 Publications have been cited 2,103 times in 1,002 Documents Cited by Year
Nonstandard finite difference models of differential equations. Zbl 0810.65083
Mickens, Ronald E.
1994
Oscillations in planar dynamic systems. Zbl 0840.34001
Mickens, Ronald E.
1996
Nonstandard finite difference schemes. Zbl 0989.65101
Mickens, Ronald E.
2000
Difference equations. Theory and applications. 2nd ed. Zbl 0949.39500
Mickens, Ronald E.
1990
Construction of a finite-difference scheme that exactly conserves energy for a mixed parity oscillator. Zbl 0925.70016
Mickens, R. E.
1994
Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. Zbl 1073.65552
Mickens, Ronald E.
2005
Advances in the applications of nonstandard finite difference schemes. Zbl 1079.65005
Mickens, Ronald E. (ed.)
2005
Nonstandard finite difference schemes for differential equations. Zbl 1010.65032
Mickens, Ronald E.
2002
Iteration procedure for determining approximate solutions to non-linear oscillator equations. Zbl 1235.70006
Mickens, R. E.
1987
An introduction to nonlinear oscillations. Zbl 0459.34002
Mickens, Ronald E.
1981
Discretizations of nonlinear differential equations using explicit nonstandard methods. Zbl 0940.65079
Mickens, Ronald E.
1999
A nonstandard finite-difference scheme for the Lotka–Volterra system. Zbl 1025.65047
Mickens, Ronald E.
2003
Exact solutions to a finite-difference model of a nonlinear reaction- advection equation: Implications for numerical analysis. Zbl 0693.65059
Mickens, Ronald E.
1989
Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094
Mickens, Ronald E.
2007
A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086
Mickens, Ronald E.; Jordan, P. M.
2004
Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085
Mickens, Ronald E.
1999
Numerical integration of population models satisfying conservation laws: NSFD methods. Zbl 1284.92116
Mickens, Ronald E.
2007
Truly nonlinear oscillations. Harmonic balance, parameter expansions, iteration, and averaging methods. Zbl 1221.34001
Mickens, Ronald E.
2010
Mathematical and numerical study of the Duffing-harmonic oscillator. Zbl 1237.65082
Mickens, R. E.
2001
Oscillations in an $$x^{4/3}$$ potential. Zbl 1237.34044
Mickens, R. E.
2001
Calculation of oscillatory properties of the solutions of two coupled, first order non-linear ordinary differential equations. Zbl 1235.34118
Mickens, R. E.
1990
A fast, stable and accurate numerical method for the Black-Scholes equation of American options. Zbl 1185.91175
Ehrhardt, Matthias; Mickens, Ronald E.
2008
A generalization of the method of harmonic balance. Zbl 1235.70154
Mickens, R. E.
1986
Iteration method solutions for conservative and limit-cycle $$x^{1/3}$$ force oscillators. Zbl 1243.34051
Mickens, R. E.
2006
A new positivity-preserving nonstandard finite difference scheme for the DWE. Zbl 1160.65329
Mickens, Ronald E.; Jordan, P. M.
2005
A best finite-difference scheme for the Fisher equation. Zbl 0810.65131
Mickens, Ronald E.
1994
A SIR-model with square-root dynamics: an NSFD scheme. Zbl 1183.92073
Mickens, Ronald E.
2010
A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”. Zbl 1243.65079
Mickens, Ronald E.
2005
Letter to the editor: Spurious limit-cycles arising in higher order averaging methods. Zbl 1232.34045
Burnette, J. E.; Mickens, R. E.
1996
A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion. Zbl 1036.65071
Mickens, R. E.
2003
Analysis of a finite-difference scheme for a linear advection-diffusion-reaction equation. Zbl 1237.76105
Mickens, R. E.
2000
Periodic solutions of the relativistic harmonic oscillator. Zbl 1235.70044
Mickens, R. E.
1998
Finite-differenc models of ordinary differential equations: Influence of denominator functions. Zbl 0695.93063
Mickens, Ronald E.; Smith, Arthur
1990
Analysis of non-linear oscillators having non-polynomial elastic terms. Zbl 1237.34065
Mickens, R. E.
2002
Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation. Zbl 0872.65080
Mickens, Ronald E.
1997
Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. Zbl 1019.65067
Chen, Z.; Gumel, A. B.; Mickens, R. E.
2003
Generalization of the method of slowly varying amplitude and phase to non-linear oscillatory systems with two degrees of freedom. Zbl 0453.70019
Mickens, R. E.
1981
Generalized harmonic balance/numerical method for determining analytical approximations to the periodic solutions of the $$x^{4/3}$$ potential. Zbl 1237.34056
Cooper, K.; Mickens, R. E.
2002
Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation. Zbl 1237.65095
Mickens, R. E.; Gumel, Abba B.
2002
A note on the delayed heat equation: instability with respect to initial data. Zbl 1258.80002
Jordan, P. M.; Dai, W.; Mickens, R. E.
2008
Exact finite-difference schemes for first order differential equations having three distinct fixed-points. Zbl 1131.65061
Roeger, Lih-Ing W.; Mickens, Ronald E.
2007
Numerical study of a non-standard finite-difference scheme for the van der Pol equation. Zbl 1237.65084
Mickens, R. E.; Gumel, A. B.
2002
Nonstandard finite difference methods. Zbl 1085.65071
Mickens, Ronald E.
2005
Exact finite difference schemes for two-dimensional advection equations. Zbl 1235.76094
Mickens, R. E.
1997
A nonstandard finite difference scheme for convection-diffusion equations having constant coefficients. Zbl 1286.65097
Ehrhardt, Matthias; Mickens, Ronald E.
2013
Exact finite difference and non-standard finite difference schemes for $$\text dx \, \text dt=-\lambda x^\alpha$$. Zbl 1260.65072
Roeger, Lih-Ing Wu; Mickens, Ronald E.
2012
A note on an NSFD scheme for a mathematical model of respiratory virus transmission. Zbl 1236.92040
Mickens, Ronald E.; Washington, Talitha M.
2012
Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. Zbl 1189.80029
Su, S.; Dai, W.; Jordan, P. M.; Mickens, R. E.
2005
Mathematical methods for the natural and engineering sciences. Zbl 1098.00003
Mickens, Ronald E.
2004
Effect of a preventive vaccine on the dynamics of HIV transmission. Zbl 1051.92038
Gumel, A. B.; Moghadas, S. M.; Mickens, R. E.
2004
A mathematical model for skin burn injury induced by radiation heating. Zbl 1151.80302
Dai, Weizhong; Wang, Haojie; Jordan, Pedro M.; Mickens, Ronald E.; Bejan, Adrian
2008
Mickens, R. E.
2004
A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. Zbl 1015.65036
Mickens, Ronald E.
2003
Suppression of numerically induced chaos with nonstandard finite difference schemes. Zbl 0931.65079
Serfaty de Markus, Alicia; Mickens, Ronald E.
1999
A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion. Zbl 1119.65374
Mickens, Ronald E.
2005
Fourier analysis of a rational harmonic balance approximation for periodic solutions. Zbl 1235.34135
Mickens, R. E.; Semwogerere, D.
1996
Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences. Zbl 1362.65084
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2014
Nonstandard finite difference schemes for Michaelis–Menten type reaction-diffusion equations. Zbl 1255.65141
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2013
Fractional van der Pol equations. Zbl 1237.34066
Mickens, R. E.
2003
A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations. Zbl 1236.34053
Mickens, R. E.
2003
Properties of finite difference models of non-linear conservative oscillators. Zbl 1235.65085
Mickens, R. E.
1988
Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV: Multi-discrete time method. Zbl 0629.39002
Mickens, Ronald E.
1987
From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes. Zbl 1252.65131
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2012
A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton’s principle. Zbl 1237.70009
Mickens, Ronald E.
2005
Solutions to the discrete Airy equation: application to parabolic equation calculations. Zbl 1060.65092
Ehrhardt, Matthias; Mickens, Ronald E.
2004
Analysis of the simple harmonic oscillator with fractional damping. Zbl 1236.70040
Mickens, R. E.; Oyedeji, Kale; Rucker, S. A.
2003
Nonstandard finite difference schemes for reaction-diffusion equations having linear advection. Zbl 0957.65081
Mickens, Ronald E.
2000
Numerical studies of a nonlinear heat equation with square root reaction term. Zbl 1165.65379
Buckmire, Ron; McMurtry, Karl; Mickens, Ronald E.
2009
Determination of denominator functions for a NSFD scheme for the Fisher PDE with linear advection. Zbl 1110.65083
Mickens, Ronald E.
2007
Investigation of the properties of the period for the nonlinear oscillator $$\ddot x+(1+\dot x^2)x=0$$. Zbl 1243.34052
Mickens, Ronald E.
2006
Exact finite difference scheme for second-order, linear ODEs having constant coefficients. Zbl 1243.65097
Mickens, Ronald E.; Oyedeji, Kale; Rucker, Sandra
2005
A nonstandard finite difference scheme for an advection-reaction equation. Zbl 1065.65109
Mickens, Ronald E.
2004
A finite difference scheme for traveling wave solutions to Burgers equation. Zbl 0929.76093
Mickens, Ronald E.
1998
Finite-difference schemes having the correct linear stability properties for all finite step-sizes. III. Zbl 0795.65040
1994
Failure of the method of slowly varying amplitude and phase for nonlinear, singular oscillators. Zbl 0925.70289
1992
Difference equation models of differential equations having zero local truncation errors. Zbl 0546.65050
Mickens, Ronald E.
1984
Calculation of order $$\varepsilon$$ dynamics for an NSFD discretization of a cube-root damped oscillator. Zbl 1292.65080
Mickens, Ronald E.
2014
A qualitative study of the solutions to the differential equation $$\ddot x+(1+\dot x^2)x=0$$. Zbl 1237.34040
Beatty, John; Mickens, Ronald E.
2005
Discrete models of differential equations: the roles of dynamic consistency and positivity. Zbl 1094.65073
Mickens, Ronald E.
2005
A non-standard finite-difference scheme for conservative oscillators. Zbl 1237.65103
Mickens, R. E.
2001
A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions. Zbl 0982.65095
Mickens, Ronald E.
2001
Applications of nonstandard finite difference schemes. Papers from the minisymposium on nonstandard finite difference schemes: theory and applications, SIAM annual meeting, Atlanta, GA, USA, 1999. Zbl 0970.00024
Mickens, Ronald E. (ed.)
2000
Investigation of a generalized van der Pol oscillator differential equation. Zbl 1237.70102
Addo-Asah, W.; Akpati, H. C.; Mickens, R. E.
1995
Exact solution to the antisymmetric, constant force oscillator equation. Zbl 0925.70259
Lipscomb, T.; Mickens, R. E.
1994
Comment on “A second-order, chaos-free, explicit method for the numerical solution of a cubic reaction problem in neurophysiology”. Zbl 0807.65095
Mickens, Ronald E.
1994
Finite-difference schemes having the correct linear stability properties for all finite step-sizes. II. Zbl 0757.65084
Mickens, Ronald E.
1992
Construction of a perturbation solution for a non-linear, singular oscillator equation. Zbl 1235.70153
Mickens, R. E.
1989
Periodic solutions of second-order nonlinear difference equations containing a small parameter. III: Perturbation theory. Zbl 0592.39005
Mickens, Ronald E.
1986
A note on the exact discretization for a Cauchy-Euler equation: application to the Black-Scholes equation. Zbl 1326.65095
Mickens, Ronald E.; Munyakazi, Justin; Washington, Talitha M.
2015
Difference equations. Theory, applications and advanced topics. 3rd ed. Zbl 1308.39001
Mickens, Ronald E.
2015
Wave front behavior of traveling wave solutions for a PDE having square-root dynamics. Zbl 1248.65111
Mickens, Ronald E.
2012
A note on a non-standard finite difference scheme for the Reluga $$x - y - z$$ model. Zbl 1205.65207
Mickens, Ronald E.
2010
Exact finite difference scheme for an advection equation having square-root dynamics. Zbl 1155.35003
Mickens, Ronald E.
2008
A note on a discretization scheme for Volterra integro-differential equations that preserves stability and boundedness. Zbl 1117.65173
Mickens, Ronald E.
2007
A non-standard finite difference scheme for the equations modelling stellar structure. Zbl 1236.85002
Mickens, R. E.
2003
Analysis of a discrete-time model for periodic diseases with pulse vaccination. Zbl 1043.39008
Mickens, Ronald E.
2003
Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis. Zbl 1037.65088
Mickens, Ronald E.
2003
A non-standard finite-difference scheme for a model of HIV transmission and control. Zbl 1036.65057
Gumel, A. B.; Mickens, R. E.; Corbett, B. D.
2003
Asymptotic solutions to a discrete Airy equation. Zbl 1005.39019
Mickens, Ronald E.
2001
Comments on “A rational harmonic balance approximation for the Duffing equation of mixed parity” (with authors’ reply). Zbl 1235.70157
Mickens, R. E.
1998
Traveling wave solutions to modified Burgers and diffusionless Fisher PDE’s. Zbl 1426.35065
Mickens, Ronald; Oyedeji, Kale
2019
Nonstandard finite difference schemes. Zbl 1378.65152
Mickens, Ronald E.
2018
Mathematical methods for the natural and engineering sciences. 2nd edition. Zbl 1357.00001
Mickens, Ronald E.
2017
Exactly solvable SIR mathematical models (some) exactly solvable SIR mathematical models. Zbl 1391.34082
Mickens, Ronald E.; Divens, Garrett
2016
A note on the exact discretization for a Cauchy-Euler equation: application to the Black-Scholes equation. Zbl 1326.65095
Mickens, Ronald E.; Munyakazi, Justin; Washington, Talitha M.
2015
Difference equations. Theory, applications and advanced topics. 3rd ed. Zbl 1308.39001
Mickens, Ronald E.
2015
Design of nonlinear isochronous oscillators. Zbl 1347.34053
Kovacic, Ivana; Mickens, Ronald E.
2015
Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences. Zbl 1362.65084
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2014
Calculation of order $$\varepsilon$$ dynamics for an NSFD discretization of a cube-root damped oscillator. Zbl 1292.65080
Mickens, Ronald E.
2014
A nonstandard finite difference scheme for convection-diffusion equations having constant coefficients. Zbl 1286.65097
Ehrhardt, Matthias; Mickens, Ronald E.
2013
Nonstandard finite difference schemes for Michaelis–Menten type reaction-diffusion equations. Zbl 1255.65141
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2013
NSFD discretizations of interacting population models satisfying conservation laws. Zbl 1350.65075
Mickens, Ronald E.; Washington, Talitha M.
2013
Exact finite difference scheme for linear differential equation with constant coefficients. Zbl 1300.65055
Roeger, Lih-Ing Wu; Mickens, Ronald E.
2013
A note on exact finite difference schemes for the differential equations satisfied by the Jacobi cosine and sine functions. Zbl 1269.65073
Mickens, Ronald E.; Washington, Talitha M.
2013
Exact finite difference and non-standard finite difference schemes for $$\text dx \, \text dt=-\lambda x^\alpha$$. Zbl 1260.65072
Roeger, Lih-Ing Wu; Mickens, Ronald E.
2012
A note on an NSFD scheme for a mathematical model of respiratory virus transmission. Zbl 1236.92040
Mickens, Ronald E.; Washington, Talitha M.
2012
From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes. Zbl 1252.65131
Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E.
2012
Wave front behavior of traveling wave solutions for a PDE having square-root dynamics. Zbl 1248.65111
Mickens, Ronald E.
2012
A generalized van der Pol type oscillator: investigation of the properties of its limit cycle. Zbl 1255.34036
Kovacic, Ivana; Mickens, Ronald E.
2012
An exactly solvable model for the spread of disease. Zbl 1248.97040
Mickens, Ronald E.
2012
An exact discretization of Michaelis-Menten type population equations. Zbl 1225.92048
Mickens, Ronald E.
2011
A nonstandard finite difference scheme for contaminant transport with kinetic Langmuir sorption. Zbl 1216.92063
Liu, Liping; Clemence, Dominic P.; Mickens, Ronald E.
2011
Truly nonlinear oscillations. Harmonic balance, parameter expansions, iteration, and averaging methods. Zbl 1221.34001
Mickens, Ronald E.
2010
A SIR-model with square-root dynamics: an NSFD scheme. Zbl 1183.92073
Mickens, Ronald E.
2010
A note on a non-standard finite difference scheme for the Reluga $$x - y - z$$ model. Zbl 1205.65207
Mickens, Ronald E.
2010
Numerical studies of a nonlinear heat equation with square root reaction term. Zbl 1165.65379
Buckmire, Ron; McMurtry, Karl; Mickens, Ronald E.
2009
Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion. Zbl 1182.65138
Mickens, Ronald E.
2009
A fast, stable and accurate numerical method for the Black-Scholes equation of American options. Zbl 1185.91175
Ehrhardt, Matthias; Mickens, Ronald E.
2008
A note on the delayed heat equation: instability with respect to initial data. Zbl 1258.80002
Jordan, P. M.; Dai, W.; Mickens, R. E.
2008
A mathematical model for skin burn injury induced by radiation heating. Zbl 1151.80302
Dai, Weizhong; Wang, Haojie; Jordan, Pedro M.; Mickens, Ronald E.; Bejan, Adrian
2008
Exact finite difference scheme for an advection equation having square-root dynamics. Zbl 1155.35003
Mickens, Ronald E.
2008
Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094
Mickens, Ronald E.
2007
Numerical integration of population models satisfying conservation laws: NSFD methods. Zbl 1284.92116
Mickens, Ronald E.
2007
Exact finite-difference schemes for first order differential equations having three distinct fixed-points. Zbl 1131.65061
Roeger, Lih-Ing W.; Mickens, Ronald E.
2007
Determination of denominator functions for a NSFD scheme for the Fisher PDE with linear advection. Zbl 1110.65083
Mickens, Ronald E.
2007
A note on a discretization scheme for Volterra integro-differential equations that preserves stability and boundedness. Zbl 1117.65173
Mickens, Ronald E.
2007
Nonstandard discretization schemes applied to the conservative Hénon-Heiles system. Zbl 1141.37381
Letellier, Christophe; Mendes, Eduardo M. A. M.; Mickens, Ronald E.
2007
Construction of nonstandard finite difference schemes for $$1\frac {1}{2}$$ space-dimension-coupled PDEs. Zbl 1107.65074
Mickens, Ronald E.; Jordan, P. M.
2007
Iteration method solutions for conservative and limit-cycle $$x^{1/3}$$ force oscillators. Zbl 1243.34051
Mickens, R. E.
2006
Investigation of the properties of the period for the nonlinear oscillator $$\ddot x+(1+\dot x^2)x=0$$. Zbl 1243.34052
Mickens, Ronald E.
2006
Mathematical studies on human disease dynamics. Emerging paradigms and challenges. AMS-IMS-SIAM joint summer research conference on modeling the dynamics of human diseases: Emerging paradigms and challenges, Snowbird, Utah, USA, July 17–21, 2005. Zbl 1103.92305
Gumel, Abba B. (ed.); Castillo-Chavez, Carlos (ed.); Mickens, Ronald E. (ed.); Clemence, Dominic P. (ed.)
2006
A nonlinear nonstandard finite difference scheme for the linear time-dependent Schrödinger equation. Zbl 1095.65088
Mickens, Ronald E.
2006
Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. Zbl 1073.65552
Mickens, Ronald E.
2005
Advances in the applications of nonstandard finite difference schemes. Zbl 1079.65005
Mickens, Ronald E. (ed.)
2005
A new positivity-preserving nonstandard finite difference scheme for the DWE. Zbl 1160.65329
Mickens, Ronald E.; Jordan, P. M.
2005
A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”. Zbl 1243.65079
Mickens, Ronald E.
2005
Nonstandard finite difference methods. Zbl 1085.65071
Mickens, Ronald E.
2005
Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. Zbl 1189.80029
Su, S.; Dai, W.; Jordan, P. M.; Mickens, R. E.
2005
A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion. Zbl 1119.65374
Mickens, Ronald E.
2005
A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton’s principle. Zbl 1237.70009
Mickens, Ronald E.
2005
Exact finite difference scheme for second-order, linear ODEs having constant coefficients. Zbl 1243.65097
Mickens, Ronald E.; Oyedeji, Kale; Rucker, Sandra
2005
A qualitative study of the solutions to the differential equation $$\ddot x+(1+\dot x^2)x=0$$. Zbl 1237.34040
Beatty, John; Mickens, Ronald E.
2005
Discrete models of differential equations: the roles of dynamic consistency and positivity. Zbl 1094.65073
Mickens, Ronald E.
2005
Reduction of computational errors using nonstandard finite difference models. Zbl 1065.65104
Serfaty de Markus, A.; Mickens, R. E.
2005
Preliminary analytical and numerical investigations of a van der Pol type oscillator having discontinuous dependence on the velocity. Zbl 1236.34054
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2005
An introduction to wave equations. Zbl 1084.35048
Mickens, Ronald E.
2005
A note on a discrete model for the harmonic oscillator Schrödinger equation in $$N$$-Cartesian coordinates. Zbl 1076.35106
Mickens, Ronald E.
2005
A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086
Mickens, Ronald E.; Jordan, P. M.
2004
Mathematical methods for the natural and engineering sciences. Zbl 1098.00003
Mickens, Ronald E.
2004
Effect of a preventive vaccine on the dynamics of HIV transmission. Zbl 1051.92038
Gumel, A. B.; Moghadas, S. M.; Mickens, R. E.
2004
Mickens, R. E.
2004
Solutions to the discrete Airy equation: application to parabolic equation calculations. Zbl 1060.65092
Ehrhardt, Matthias; Mickens, Ronald E.
2004
A nonstandard finite difference scheme for an advection-reaction equation. Zbl 1065.65109
Mickens, Ronald E.
2004
Nonstandard finite difference schemes for scalar advection-reaction partial differential equation. Zbl 1071.65123
Mickens, Ronald E.
2004
Construction of a discrete-time model for periodic diseases with integer-valued populations. Zbl 1054.92043
Mickens, Ronald E.
2004
A nonstandard finite-difference scheme for the Lotka–Volterra system. Zbl 1025.65047
Mickens, Ronald E.
2003
A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion. Zbl 1036.65071
Mickens, R. E.
2003
Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. Zbl 1019.65067
Chen, Z.; Gumel, A. B.; Mickens, R. E.
2003
A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. Zbl 1015.65036
Mickens, Ronald E.
2003
Fractional van der Pol equations. Zbl 1237.34066
Mickens, R. E.
2003
A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations. Zbl 1236.34053
Mickens, R. E.
2003
Analysis of the simple harmonic oscillator with fractional damping. Zbl 1236.70040
Mickens, R. E.; Oyedeji, Kale; Rucker, S. A.
2003
A non-standard finite difference scheme for the equations modelling stellar structure. Zbl 1236.85002
Mickens, R. E.
2003
Analysis of a discrete-time model for periodic diseases with pulse vaccination. Zbl 1043.39008
Mickens, Ronald E.
2003
Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis. Zbl 1037.65088
Mickens, Ronald E.
2003
A non-standard finite-difference scheme for a model of HIV transmission and control. Zbl 1036.65057
Gumel, A. B.; Mickens, R. E.; Corbett, B. D.
2003
Positivity preserving discrete model for the coupled ODE’s modeling glycolysis. Zbl 1060.65071
Mickens, Ronald E.
2003
Nonstandard finite difference schemes for differential equations. Zbl 1010.65032
Mickens, Ronald E.
2002
Analysis of non-linear oscillators having non-polynomial elastic terms. Zbl 1237.34065
Mickens, R. E.
2002
Generalized harmonic balance/numerical method for determining analytical approximations to the periodic solutions of the $$x^{4/3}$$ potential. Zbl 1237.34056
Cooper, K.; Mickens, R. E.
2002
Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation. Zbl 1237.65095
Mickens, R. E.; Gumel, Abba B.
2002
Numerical study of a non-standard finite-difference scheme for the van der Pol equation. Zbl 1237.65084
Mickens, R. E.; Gumel, A. B.
2002
Step-size dependence of the period for a forward-Euler scheme of the van der Pol equation. Zbl 1237.65083
Mickens, R. E.
2002
Mathematical and numerical study of the Duffing-harmonic oscillator. Zbl 1237.65082
Mickens, R. E.
2001
Oscillations in an $$x^{4/3}$$ potential. Zbl 1237.34044
Mickens, R. E.
2001
A non-standard finite-difference scheme for conservative oscillators. Zbl 1237.65103
Mickens, R. E.
2001
A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions. Zbl 0982.65095
Mickens, Ronald E.
2001
Asymptotic solutions to a discrete Airy equation. Zbl 1005.39019
Mickens, Ronald E.
2001
Analytical and numerical study of a non-standard finite difference scheme for the unplugged Van der pol equation. Zbl 1237.65074
Mickens, R. E.
2001
A particular exact solution to the central core model of the renal medulla. Zbl 0999.92015
Mickens, R. E.
2001
Nonstandard finite difference schemes. Zbl 0989.65101
Mickens, Ronald E.
2000
Analysis of a finite-difference scheme for a linear advection-diffusion-reaction equation. Zbl 1237.76105
Mickens, R. E.
2000
Nonstandard finite difference schemes for reaction-diffusion equations having linear advection. Zbl 0957.65081
Mickens, Ronald E.
2000
Applications of nonstandard finite difference schemes. Papers from the minisymposium on nonstandard finite difference schemes: theory and applications, SIAM annual meeting, Atlanta, GA, USA, 1999. Zbl 0970.00024
Mickens, Ronald E. (ed.)
2000
Generalized harmonic oscillators. Zbl 1237.70112
Mickens, Ronald E.
2000
An order $$\varepsilon^2$$ perturbation procedure for second-order nonlinear difference equations. Zbl 0963.39005
Mickens, Ronald E.
2000
Discretizations of nonlinear differential equations using explicit nonstandard methods. Zbl 0940.65079
Mickens, Ronald E.
1999
Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085
Mickens, Ronald E.
1999
Suppression of numerically induced chaos with nonstandard finite difference schemes. Zbl 0931.65079
Serfaty de Markus, Alicia; Mickens, Ronald E.
1999
An introduction to nonstandard finite difference schemes. Zbl 1360.65007
Mickens, Ronald E.
1999
...and 61 more Documents
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#### Cited by 1,339 Authors

 79 Mickens, Ronald Elbert 41 Macías-Díaz, Jorge Eduardo 29 Lubuma, Jean Mbaro-Saman 23 Beléndez, Augusto 18 Patidar, Kailash C. 17 Ding, Xiaohua 15 Roeger, Lih-Ing Wu 14 Ramos, Juan I. 13 Kojouharov, Hristo V. 12 Anguelov, Roumen 12 Beléndez, Tarsicio 10 Jordan, Pedro M. 9 Álvarez, Mariela L. 9 Chapwanya, Michael 9 Ganji, Davood Domiri 9 Kovacic, Ivana 8 Arenas, Abraham J. 8 Arribas, Enrique 8 Chen-Charpentier, Benito M. 8 Dehghan Takht Fooladi, Mehdi 8 Gumel, Abba B. 8 Hoang, Manh Tuan 8 Pascual, Carolina 8 Shi, Haiping 8 Straughan, Brian 8 Sweilam, Nasser Hassan 8 Wang, Zhongcheng 7 Băleanu, Dumitru I. 7 Dimitrov, Dobromir T. 7 Ding, Deqiong 7 Djoko, Jules K. 7 Dumont, Yves 7 González-Parra, Gilberto C. 7 Jódar Sanchez, Lucas Antonio 7 Marinca, Vasile 7 Tarasov, Vasily E. 7 Teng, Zhi-dong 7 Xu, Jinhu 7 Yıldırım, Ahmet 6 Company, Rafael 6 Cveticanin, Livija 6 Deng, Xiaoqing 6 Geng, Yan 6 Herişanu, Nicolae 6 Liu, Xia 6 Méndez, D. I. 6 Mohamad, Sannay 6 Momani, Shaher M. 6 Rafiq, Muhammad 6 Wang, Yuanyuan 5 Agarwal, Ravi P. 5 Appadu, A. R. 5 Askari, Hassan Randjbar 5 Cveticanin, L. J. 5 Dang Quang A 5 Ehrhardt, Matthias 5 Elías-Zúñiga, Alex 5 Francés, Jorge 5 Gimeno, Encarnación 5 Gopalsamy, Kondalsamy 5 Lai, Siu Kai 5 Moaddy, Khaled 5 Moghadas, Seyed M. 5 Munyakazi, Justin B. 5 Pascual, Inmaculada 5 Puri, Ashok 5 Qin, Wendi 5 Sharma, Kapil Kumar 5 Solís, Francisco Javier 5 Terefe, Yibeltal Adane 5 Washington, Talitha Michal 5 Zhang, Yuanbiao 4 Ahmed, Nauman 4 Al-Mekhlafi, Seham Mahyoub 4 Aleksandrov, Aleksandr Yur’evich 4 Ciarletta, Michele 4 Cieśliński, Jan L. 4 Clemence, Dominic P. 4 Dai, Yongming 4 Din, Qamar 4 Elaydi, Saber Nasr 4 Fakharany, M. 4 Ganji, S. S. 4 Guo, Zhongjin 4 Hashim, Ishak 4 Kumar Roy, Priti 4 Lai, Samuel K. 4 Lim, Chi Wan 4 Lim, Chia Wei 4 Medina-Ramírez, Iliana E. 4 Mittal, Ramesh Chand 4 Neipp, C. 4 Ozis, Turgut 4 Philos, Christos G. 4 Purnaras, Ioannis K. 4 Quintanilla de Latorre, Ramón 4 Rakaric, Zvonko 4 Ramos, Higinio 4 Rehman, Muhammad Aziz-Ur 4 Ruiz-Ramírez, Javier ...and 1,239 more Authors
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#### Cited in 196 Serials

 107 Journal of Difference Equations and Applications 77 Applied Mathematics and Computation 67 Computers & Mathematics with Applications 52 Journal of Computational and Applied Mathematics 32 Advances in Difference Equations 29 Numerical Methods for Partial Differential Equations 25 Chaos, Solitons and Fractals 25 International Journal of Computer Mathematics 22 Nonlinear Dynamics 21 Communications in Nonlinear Science and Numerical Simulation 16 Mathematical Methods in the Applied Sciences 16 Mathematics and Computers in Simulation 16 Applied Mathematical Modelling 16 Journal of Applied Mathematics 15 Physics Letters. A 14 Mathematical and Computer Modelling 13 Journal of Computational Physics 12 Applied Numerical Mathematics 12 Computational and Applied Mathematics 11 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Journal of the Franklin Institute 10 Journal of Mathematical Analysis and Applications 9 Acta Mechanica 9 Mechanics Research Communications 9 International Journal of Applied and Computational Mathematics 8 Applied Mathematics Letters 8 Nonlinear Analysis. Real World Applications 7 Computer Physics Communications 7 Abstract and Applied Analysis 7 Discrete Dynamics in Nature and Society 6 Acta Applicandae Mathematicae 6 Journal of the Egyptian Mathematical Society 6 Journal of Mathematical Chemistry 6 Qualitative Theory of Dynamical Systems 6 Journal of Biological Dynamics 5 International Journal of Heat and Mass Transfer 5 Journal of Mathematical Physics 5 Mathematical Biosciences 5 Numerical Algorithms 5 Discrete and Continuous Dynamical Systems. Series B 5 International Journal of Biomathematics 5 Journal of Theoretical Biology 4 Applicable Analysis 4 Journal of Mathematical Biology 4 Meccanica 4 Applied Mathematics and Mechanics. (English Edition) 4 Physica D 4 Mathematical Problems in Engineering 4 Journal of Vibration and Control 4 Chaos 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 International Journal of Modern Physics B 3 International Journal of Control 3 International Journal of Engineering Science 3 International Journal of Mathematics and Mathematical Sciences 3 International Journal for Numerical Methods in Engineering 3 Journal of Differential Equations 3 Journal of Scientific Computing 3 Archive of Applied Mechanics 3 Differential Equations and Dynamical Systems 3 International Journal of Applied Mathematics and Computer Science 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Journal of Applied Mathematics and Computing 3 International Journal of Computational Methods 3 Mediterranean Journal of Mathematics 3 Mathematical Biosciences and Engineering 3 Asian-European Journal of Mathematics 3 Advances in Mathematical Physics 3 International Journal of Differential Equations 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Engineering Mathematics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Bulletin of Mathematical Biology 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Numerical Functional Analysis and Optimization 2 Ricerche di Matematica 2 Theoretical Computer Science 2 Acta Mathematica Hungarica 2 Acta Mathematicae Applicatae Sinica. English Series 2 Dynamics and Stability of Systems 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 2 Automation and Remote Control 2 Journal of Mathematical Imaging and Vision 2 Journal of Interdisciplinary Mathematics 2 Journal of Biological Systems 2 International Journal of Modern Physics C 2 The ANZIAM Journal 2 Annales Universitatis Mariae Curie-Skłodowska. Sectio A1. Informatica 2 Discrete and Continuous Dynamical Systems. Series S 2 International Journal for Numerical Methods in Biomedical Engineering 2 Afrika Matematika 2 Mathematical Sciences 2 Evolution Equations and Control Theory 2 International Journal of Analysis and Applications 2 Computational Methods for Differential Equations 1 Modern Physics Letters A 1 Modern Physics Letters B 1 Bulletin of the Australian Mathematical Society ...and 96 more Serials
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#### Cited in 43 Fields

 514 Numerical analysis (65-XX) 337 Ordinary differential equations (34-XX) 232 Biology and other natural sciences (92-XX) 226 Partial differential equations (35-XX) 161 Difference and functional equations (39-XX) 103 Dynamical systems and ergodic theory (37-XX) 78 Mechanics of particles and systems (70-XX) 40 Mechanics of deformable solids (74-XX) 34 Fluid mechanics (76-XX) 34 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 34 Systems theory; control (93-XX) 31 Classical thermodynamics, heat transfer (80-XX) 22 Real functions (26-XX) 18 Integral equations (45-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 16 Probability theory and stochastic processes (60-XX) 13 Quantum theory (81-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Operator theory (47-XX) 10 Optics, electromagnetic theory (78-XX) 9 Computer science (68-XX) 8 Information and communication theory, circuits (94-XX) 6 Operations research, mathematical programming (90-XX) 5 General and overarching topics; collections (00-XX) 5 Special functions (33-XX) 5 Statistics (62-XX) 4 Approximations and expansions (41-XX) 3 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Integral transforms, operational calculus (44-XX) 2 Measure and integration (28-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX)