Edit Profile Mickens, Ronald Elbert Compute Distance To: Compute 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 all top 5 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. all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0810.65083Mickens, Ronald E. 286 1994 Oscillations in planar dynamic systems. Zbl 0840.34001Mickens, Ronald E. 94 1996 Nonstandard finite difference schemes. Zbl 0989.65101Mickens, Ronald E. 86 2000 Difference equations. Theory and applications. 2nd ed. Zbl 0949.39500Mickens, Ronald E. 71 1990 Construction of a finite-difference scheme that exactly conserves energy for a mixed parity oscillator. Zbl 0925.70016Mickens, R. E. 69 1994 Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. Zbl 1073.65552Mickens, Ronald E. 65 2005 Advances in the applications of nonstandard finite difference schemes. Zbl 1079.65005Mickens, Ronald E. (ed.) 61 2005 Nonstandard finite difference schemes for differential equations. Zbl 1010.65032Mickens, Ronald E. 54 2002 Iteration procedure for determining approximate solutions to non-linear oscillator equations. Zbl 1235.70006Mickens, R. E. 54 1987 An introduction to nonlinear oscillations. Zbl 0459.34002Mickens, Ronald E. 52 1981 Discretizations of nonlinear differential equations using explicit nonstandard methods. Zbl 0940.65079Mickens, Ronald E. 49 1999 A nonstandard finite-difference scheme for the Lotka–Volterra system. Zbl 1025.65047Mickens, Ronald E. 45 2003 Exact solutions to a finite-difference model of a nonlinear reaction- advection equation: Implications for numerical analysis. Zbl 0693.65059Mickens, Ronald E. 43 1989 Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094Mickens, Ronald E. 42 2007 A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086Mickens, Ronald E.; Jordan, P. M. 38 2004 Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085Mickens, Ronald E. 31 1999 Numerical integration of population models satisfying conservation laws: NSFD methods. Zbl 1284.92116Mickens, Ronald E. 30 2007 Truly nonlinear oscillations. Harmonic balance, parameter expansions, iteration, and averaging methods. Zbl 1221.34001Mickens, Ronald E. 29 2010 Mathematical and numerical study of the Duffing-harmonic oscillator. Zbl 1237.65082Mickens, R. E. 27 2001 Oscillations in an \(x^{4/3}\) potential. Zbl 1237.34044Mickens, R. E. 26 2001 Calculation of oscillatory properties of the solutions of two coupled, first order non-linear ordinary differential equations. Zbl 1235.34118Mickens, R. E. 26 1990 A fast, stable and accurate numerical method for the Black-Scholes equation of American options. Zbl 1185.91175Ehrhardt, Matthias; Mickens, Ronald E. 25 2008 A generalization of the method of harmonic balance. Zbl 1235.70154Mickens, R. E. 24 1986 Iteration method solutions for conservative and limit-cycle \(x^{1/3}\) force oscillators. Zbl 1243.34051Mickens, R. E. 23 2006 A new positivity-preserving nonstandard finite difference scheme for the DWE. Zbl 1160.65329Mickens, Ronald E.; Jordan, P. M. 22 2005 A best finite-difference scheme for the Fisher equation. Zbl 0810.65131Mickens, Ronald E. 22 1994 A SIR-model with square-root dynamics: an NSFD scheme. Zbl 1183.92073Mickens, Ronald E. 20 2010 A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”. Zbl 1243.65079Mickens, Ronald E. 20 2005 Letter to the editor: Spurious limit-cycles arising in higher order averaging methods. Zbl 1232.34045Burnette, J. E.; Mickens, R. E. 20 1996 A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion. Zbl 1036.65071Mickens, R. E. 19 2003 Analysis of a finite-difference scheme for a linear advection-diffusion-reaction equation. Zbl 1237.76105Mickens, R. E. 19 2000 Periodic solutions of the relativistic harmonic oscillator. Zbl 1235.70044Mickens, R. E. 19 1998 Finite-differenc models of ordinary differential equations: Influence of denominator functions. Zbl 0695.93063Mickens, Ronald E.; Smith, Arthur 19 1990 Analysis of non-linear oscillators having non-polynomial elastic terms. Zbl 1237.34065Mickens, R. E. 18 2002 Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation. Zbl 0872.65080Mickens, Ronald E. 18 1997 Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. Zbl 1019.65067Chen, Z.; Gumel, A. B.; Mickens, R. E. 17 2003 Generalization of the method of slowly varying amplitude and phase to non-linear oscillatory systems with two degrees of freedom. Zbl 0453.70019Mickens, R. E. 17 1981 Generalized harmonic balance/numerical method for determining analytical approximations to the periodic solutions of the \(x^{4/3}\) potential. Zbl 1237.34056Cooper, K.; Mickens, R. E. 15 2002 Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation. Zbl 1237.65095Mickens, R. E.; Gumel, Abba B. 14 2002 A note on the delayed heat equation: instability with respect to initial data. Zbl 1258.80002Jordan, P. M.; Dai, W.; Mickens, R. E. 13 2008 Exact finite-difference schemes for first order differential equations having three distinct fixed-points. Zbl 1131.65061Roeger, Lih-Ing W.; Mickens, Ronald E. 12 2007 Numerical study of a non-standard finite-difference scheme for the van der Pol equation. Zbl 1237.65084Mickens, R. E.; Gumel, A. B. 12 2002 Nonstandard finite difference methods. Zbl 1085.65071Mickens, Ronald E. 11 2005 Exact finite difference schemes for two-dimensional advection equations. Zbl 1235.76094Mickens, R. E. 11 1997 A nonstandard finite difference scheme for convection-diffusion equations having constant coefficients. Zbl 1286.65097Ehrhardt, Matthias; Mickens, Ronald E. 10 2013 Exact finite difference and non-standard finite difference schemes for \(\text dx \, \text dt=-\lambda x^\alpha\). Zbl 1260.65072Roeger, Lih-Ing Wu; Mickens, Ronald E. 10 2012 A note on an NSFD scheme for a mathematical model of respiratory virus transmission. Zbl 1236.92040Mickens, Ronald E.; Washington, Talitha M. 10 2012 Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. Zbl 1189.80029Su, S.; Dai, W.; Jordan, P. M.; Mickens, R. E. 10 2005 Mathematical methods for the natural and engineering sciences. Zbl 1098.00003Mickens, Ronald E. 10 2004 Effect of a preventive vaccine on the dynamics of HIV transmission. Zbl 1051.92038Gumel, A. B.; Moghadas, S. M.; Mickens, R. E. 10 2004 A mathematical model for skin burn injury induced by radiation heating. Zbl 1151.80302Dai, Weizhong; Wang, Haojie; Jordan, Pedro M.; Mickens, Ronald E.; Bejan, Adrian 9 2008 Quadratic non-linear oscillators. Zbl 1236.70036Mickens, R. E. 9 2004 A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. Zbl 1015.65036Mickens, Ronald E. 9 2003 Suppression of numerically induced chaos with nonstandard finite difference schemes. Zbl 0931.65079Serfaty de Markus, Alicia; Mickens, Ronald E. 9 1999 A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion. Zbl 1119.65374Mickens, Ronald E. 8 2005 Fourier analysis of a rational harmonic balance approximation for periodic solutions. Zbl 1235.34135Mickens, R. E.; Semwogerere, D. 8 1996 Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences. Zbl 1362.65084Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 7 2014 Nonstandard finite difference schemes for Michaelis–Menten type reaction-diffusion equations. Zbl 1255.65141Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 7 2013 Fractional van der Pol equations. Zbl 1237.34066Mickens, R. E. 7 2003 A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations. Zbl 1236.34053Mickens, R. E. 7 2003 Properties of finite difference models of non-linear conservative oscillators. Zbl 1235.65085Mickens, R. E. 7 1988 Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV: Multi-discrete time method. Zbl 0629.39002Mickens, Ronald E. 7 1987 From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes. Zbl 1252.65131Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 6 2012 A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton’s principle. Zbl 1237.70009Mickens, Ronald E. 6 2005 Solutions to the discrete Airy equation: application to parabolic equation calculations. Zbl 1060.65092Ehrhardt, Matthias; Mickens, Ronald E. 6 2004 Analysis of the simple harmonic oscillator with fractional damping. Zbl 1236.70040Mickens, R. E.; Oyedeji, Kale; Rucker, S. A. 6 2003 Nonstandard finite difference schemes for reaction-diffusion equations having linear advection. Zbl 0957.65081Mickens, Ronald E. 6 2000 Numerical studies of a nonlinear heat equation with square root reaction term. Zbl 1165.65379Buckmire, Ron; McMurtry, Karl; Mickens, Ronald E. 5 2009 Determination of denominator functions for a NSFD scheme for the Fisher PDE with linear advection. Zbl 1110.65083Mickens, Ronald E. 5 2007 Investigation of the properties of the period for the nonlinear oscillator \(\ddot x+(1+\dot x^2)x=0\). Zbl 1243.34052Mickens, Ronald E. 5 2006 Exact finite difference scheme for second-order, linear ODEs having constant coefficients. Zbl 1243.65097Mickens, Ronald E.; Oyedeji, Kale; Rucker, Sandra 5 2005 A nonstandard finite difference scheme for an advection-reaction equation. Zbl 1065.65109Mickens, Ronald E. 5 2004 A finite difference scheme for traveling wave solutions to Burgers equation. Zbl 0929.76093Mickens, Ronald E. 5 1998 Finite-difference schemes having the correct linear stability properties for all finite step-sizes. III. Zbl 0795.65040Mickens, R. E.; Ramadhani, I. 5 1994 Failure of the method of slowly varying amplitude and phase for nonlinear, singular oscillators. Zbl 0925.70289Mickens, R. E.; Ramadhani, I. 5 1992 Difference equation models of differential equations having zero local truncation errors. Zbl 0546.65050Mickens, Ronald E. 5 1984 Calculation of order \(\varepsilon\) dynamics for an NSFD discretization of a cube-root damped oscillator. Zbl 1292.65080Mickens, Ronald E. 4 2014 A qualitative study of the solutions to the differential equation \(\ddot x+(1+\dot x^2)x=0\). Zbl 1237.34040Beatty, John; Mickens, Ronald E. 4 2005 Discrete models of differential equations: the roles of dynamic consistency and positivity. Zbl 1094.65073Mickens, Ronald E. 4 2005 A non-standard finite-difference scheme for conservative oscillators. Zbl 1237.65103Mickens, R. E. 4 2001 A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions. Zbl 0982.65095Mickens, Ronald E. 4 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 0970.00024Mickens, Ronald E. (ed.) 4 2000 Investigation of a generalized van der Pol oscillator differential equation. Zbl 1237.70102Addo-Asah, W.; Akpati, H. C.; Mickens, R. E. 4 1995 Exact solution to the antisymmetric, constant force oscillator equation. Zbl 0925.70259Lipscomb, T.; Mickens, R. E. 4 1994 Comment on “A second-order, chaos-free, explicit method for the numerical solution of a cubic reaction problem in neurophysiology”. Zbl 0807.65095Mickens, Ronald E. 4 1994 Finite-difference schemes having the correct linear stability properties for all finite step-sizes. II. Zbl 0757.65084Mickens, Ronald E. 4 1992 Construction of a perturbation solution for a non-linear, singular oscillator equation. Zbl 1235.70153Mickens, R. E. 4 1989 Periodic solutions of second-order nonlinear difference equations containing a small parameter. III: Perturbation theory. Zbl 0592.39005Mickens, Ronald E. 4 1986 A note on the exact discretization for a Cauchy-Euler equation: application to the Black-Scholes equation. Zbl 1326.65095Mickens, Ronald E.; Munyakazi, Justin; Washington, Talitha M. 3 2015 Difference equations. Theory, applications and advanced topics. 3rd ed. Zbl 1308.39001Mickens, Ronald E. 3 2015 Wave front behavior of traveling wave solutions for a PDE having square-root dynamics. Zbl 1248.65111Mickens, Ronald E. 3 2012 A note on a non-standard finite difference scheme for the Reluga \(x - y - z\) model. Zbl 1205.65207Mickens, Ronald E. 3 2010 Exact finite difference scheme for an advection equation having square-root dynamics. Zbl 1155.35003Mickens, Ronald E. 3 2008 A note on a discretization scheme for Volterra integro-differential equations that preserves stability and boundedness. Zbl 1117.65173Mickens, Ronald E. 3 2007 A non-standard finite difference scheme for the equations modelling stellar structure. Zbl 1236.85002Mickens, R. E. 3 2003 Analysis of a discrete-time model for periodic diseases with pulse vaccination. Zbl 1043.39008Mickens, Ronald E. 3 2003 Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis. Zbl 1037.65088Mickens, Ronald E. 3 2003 A non-standard finite-difference scheme for a model of HIV transmission and control. Zbl 1036.65057Gumel, A. B.; Mickens, R. E.; Corbett, B. D. 3 2003 Asymptotic solutions to a discrete Airy equation. Zbl 1005.39019Mickens, Ronald E. 3 2001 Comments on “A rational harmonic balance approximation for the Duffing equation of mixed parity” (with authors’ reply). Zbl 1235.70157Mickens, R. E. 3 1998 Traveling wave solutions to modified Burgers and diffusionless Fisher PDE’s. Zbl 1426.35065Mickens, Ronald; Oyedeji, Kale 1 2019 Nonstandard finite difference schemes. Zbl 1378.65152Mickens, Ronald E. 1 2018 Mathematical methods for the natural and engineering sciences. 2nd edition. Zbl 1357.00001Mickens, Ronald E. 1 2017 Exactly solvable SIR mathematical models (some) exactly solvable SIR mathematical models. Zbl 1391.34082Mickens, Ronald E.; Divens, Garrett 1 2016 A note on the exact discretization for a Cauchy-Euler equation: application to the Black-Scholes equation. Zbl 1326.65095Mickens, Ronald E.; Munyakazi, Justin; Washington, Talitha M. 3 2015 Difference equations. Theory, applications and advanced topics. 3rd ed. Zbl 1308.39001Mickens, Ronald E. 3 2015 Design of nonlinear isochronous oscillators. Zbl 1347.34053Kovacic, Ivana; Mickens, Ronald E. 1 2015 Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences. Zbl 1362.65084Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 7 2014 Calculation of order \(\varepsilon\) dynamics for an NSFD discretization of a cube-root damped oscillator. Zbl 1292.65080Mickens, Ronald E. 4 2014 A nonstandard finite difference scheme for convection-diffusion equations having constant coefficients. Zbl 1286.65097Ehrhardt, Matthias; Mickens, Ronald E. 10 2013 Nonstandard finite difference schemes for Michaelis–Menten type reaction-diffusion equations. Zbl 1255.65141Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 7 2013 NSFD discretizations of interacting population models satisfying conservation laws. Zbl 1350.65075Mickens, Ronald E.; Washington, Talitha M. 2 2013 Exact finite difference scheme for linear differential equation with constant coefficients. Zbl 1300.65055Roeger, Lih-Ing Wu; Mickens, Ronald E. 2 2013 A note on exact finite difference schemes for the differential equations satisfied by the Jacobi cosine and sine functions. Zbl 1269.65073Mickens, Ronald E.; Washington, Talitha M. 2 2013 Exact finite difference and non-standard finite difference schemes for \(\text dx \, \text dt=-\lambda x^\alpha\). Zbl 1260.65072Roeger, Lih-Ing Wu; Mickens, Ronald E. 10 2012 A note on an NSFD scheme for a mathematical model of respiratory virus transmission. Zbl 1236.92040Mickens, Ronald E.; Washington, Talitha M. 10 2012 From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes. Zbl 1252.65131Chapwanya, Michael; Lubuma, Jean M.-S.; Mickens, Ronald E. 6 2012 Wave front behavior of traveling wave solutions for a PDE having square-root dynamics. Zbl 1248.65111Mickens, Ronald E. 3 2012 A generalized van der Pol type oscillator: investigation of the properties of its limit cycle. Zbl 1255.34036Kovacic, Ivana; Mickens, Ronald E. 1 2012 An exactly solvable model for the spread of disease. Zbl 1248.97040Mickens, Ronald E. 1 2012 An exact discretization of Michaelis-Menten type population equations. Zbl 1225.92048Mickens, Ronald E. 2 2011 A nonstandard finite difference scheme for contaminant transport with kinetic Langmuir sorption. Zbl 1216.92063Liu, Liping; Clemence, Dominic P.; Mickens, Ronald E. 2 2011 Truly nonlinear oscillations. Harmonic balance, parameter expansions, iteration, and averaging methods. Zbl 1221.34001Mickens, Ronald E. 29 2010 A SIR-model with square-root dynamics: an NSFD scheme. Zbl 1183.92073Mickens, Ronald E. 20 2010 A note on a non-standard finite difference scheme for the Reluga \(x - y - z\) model. Zbl 1205.65207Mickens, Ronald E. 3 2010 Numerical studies of a nonlinear heat equation with square root reaction term. Zbl 1165.65379Buckmire, Ron; McMurtry, Karl; Mickens, Ronald E. 5 2009 Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion. Zbl 1182.65138Mickens, Ronald E. 2 2009 A fast, stable and accurate numerical method for the Black-Scholes equation of American options. Zbl 1185.91175Ehrhardt, Matthias; Mickens, Ronald E. 25 2008 A note on the delayed heat equation: instability with respect to initial data. Zbl 1258.80002Jordan, P. M.; Dai, W.; Mickens, R. E. 13 2008 A mathematical model for skin burn injury induced by radiation heating. Zbl 1151.80302Dai, Weizhong; Wang, Haojie; Jordan, Pedro M.; Mickens, Ronald E.; Bejan, Adrian 9 2008 Exact finite difference scheme for an advection equation having square-root dynamics. Zbl 1155.35003Mickens, Ronald E. 3 2008 Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094Mickens, Ronald E. 42 2007 Numerical integration of population models satisfying conservation laws: NSFD methods. Zbl 1284.92116Mickens, Ronald E. 30 2007 Exact finite-difference schemes for first order differential equations having three distinct fixed-points. Zbl 1131.65061Roeger, Lih-Ing W.; Mickens, Ronald E. 12 2007 Determination of denominator functions for a NSFD scheme for the Fisher PDE with linear advection. Zbl 1110.65083Mickens, Ronald E. 5 2007 A note on a discretization scheme for Volterra integro-differential equations that preserves stability and boundedness. Zbl 1117.65173Mickens, Ronald E. 3 2007 Nonstandard discretization schemes applied to the conservative Hénon-Heiles system. Zbl 1141.37381Letellier, Christophe; Mendes, Eduardo M. A. M.; Mickens, Ronald E. 2 2007 Construction of nonstandard finite difference schemes for \(1\frac {1}{2}\) space-dimension-coupled PDEs. Zbl 1107.65074Mickens, Ronald E.; Jordan, P. M. 2 2007 Iteration method solutions for conservative and limit-cycle \(x^{1/3}\) force oscillators. Zbl 1243.34051Mickens, R. E. 23 2006 Investigation of the properties of the period for the nonlinear oscillator \(\ddot x+(1+\dot x^2)x=0\). Zbl 1243.34052Mickens, Ronald E. 5 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 1103.92305Gumel, Abba B. (ed.); Castillo-Chavez, Carlos (ed.); Mickens, Ronald E. (ed.); Clemence, Dominic P. (ed.) 2 2006 A nonlinear nonstandard finite difference scheme for the linear time-dependent Schrödinger equation. Zbl 1095.65088Mickens, Ronald E. 2 2006 Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. Zbl 1073.65552Mickens, Ronald E. 65 2005 Advances in the applications of nonstandard finite difference schemes. Zbl 1079.65005Mickens, Ronald E. (ed.) 61 2005 A new positivity-preserving nonstandard finite difference scheme for the DWE. Zbl 1160.65329Mickens, Ronald E.; Jordan, P. M. 22 2005 A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”. Zbl 1243.65079Mickens, Ronald E. 20 2005 Nonstandard finite difference methods. Zbl 1085.65071Mickens, Ronald E. 11 2005 Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. Zbl 1189.80029Su, S.; Dai, W.; Jordan, P. M.; Mickens, R. E. 10 2005 A nonstandard finite difference scheme for a PDE modeling combustion with nonlinear advection and diffusion. Zbl 1119.65374Mickens, Ronald E. 8 2005 A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton’s principle. Zbl 1237.70009Mickens, Ronald E. 6 2005 Exact finite difference scheme for second-order, linear ODEs having constant coefficients. Zbl 1243.65097Mickens, Ronald E.; Oyedeji, Kale; Rucker, Sandra 5 2005 A qualitative study of the solutions to the differential equation \(\ddot x+(1+\dot x^2)x=0\). Zbl 1237.34040Beatty, John; Mickens, Ronald E. 4 2005 Discrete models of differential equations: the roles of dynamic consistency and positivity. Zbl 1094.65073Mickens, Ronald E. 4 2005 Reduction of computational errors using nonstandard finite difference models. Zbl 1065.65104Serfaty de Markus, A.; Mickens, R. E. 2 2005 Preliminary analytical and numerical investigations of a van der Pol type oscillator having discontinuous dependence on the velocity. Zbl 1236.34054Mickens, R. E.; Oyedeji, K.; Rucker, S. A. 1 2005 An introduction to wave equations. Zbl 1084.35048Mickens, Ronald E. 1 2005 A note on a discrete model for the harmonic oscillator Schrödinger equation in \(N\)-Cartesian coordinates. Zbl 1076.35106Mickens, Ronald E. 1 2005 A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086Mickens, Ronald E.; Jordan, P. M. 38 2004 Mathematical methods for the natural and engineering sciences. Zbl 1098.00003Mickens, Ronald E. 10 2004 Effect of a preventive vaccine on the dynamics of HIV transmission. Zbl 1051.92038Gumel, A. B.; Moghadas, S. M.; Mickens, R. E. 10 2004 Quadratic non-linear oscillators. Zbl 1236.70036Mickens, R. E. 9 2004 Solutions to the discrete Airy equation: application to parabolic equation calculations. Zbl 1060.65092Ehrhardt, Matthias; Mickens, Ronald E. 6 2004 A nonstandard finite difference scheme for an advection-reaction equation. Zbl 1065.65109Mickens, Ronald E. 5 2004 Nonstandard finite difference schemes for scalar advection-reaction partial differential equation. Zbl 1071.65123Mickens, Ronald E. 1 2004 Construction of a discrete-time model for periodic diseases with integer-valued populations. Zbl 1054.92043Mickens, Ronald E. 1 2004 A nonstandard finite-difference scheme for the Lotka–Volterra system. Zbl 1025.65047Mickens, Ronald E. 45 2003 A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion. Zbl 1036.65071Mickens, R. E. 19 2003 Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. Zbl 1019.65067Chen, Z.; Gumel, A. B.; Mickens, R. E. 17 2003 A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. Zbl 1015.65036Mickens, Ronald E. 9 2003 Fractional van der Pol equations. Zbl 1237.34066Mickens, R. E. 7 2003 A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations. Zbl 1236.34053Mickens, R. E. 7 2003 Analysis of the simple harmonic oscillator with fractional damping. Zbl 1236.70040Mickens, R. E.; Oyedeji, Kale; Rucker, S. A. 6 2003 A non-standard finite difference scheme for the equations modelling stellar structure. Zbl 1236.85002Mickens, R. E. 3 2003 Analysis of a discrete-time model for periodic diseases with pulse vaccination. Zbl 1043.39008Mickens, Ronald E. 3 2003 Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis. Zbl 1037.65088Mickens, Ronald E. 3 2003 A non-standard finite-difference scheme for a model of HIV transmission and control. Zbl 1036.65057Gumel, A. B.; Mickens, R. E.; Corbett, B. D. 3 2003 Positivity preserving discrete model for the coupled ODE’s modeling glycolysis. Zbl 1060.65071Mickens, Ronald E. 2 2003 Nonstandard finite difference schemes for differential equations. Zbl 1010.65032Mickens, Ronald E. 54 2002 Analysis of non-linear oscillators having non-polynomial elastic terms. Zbl 1237.34065Mickens, R. E. 18 2002 Generalized harmonic balance/numerical method for determining analytical approximations to the periodic solutions of the \(x^{4/3}\) potential. Zbl 1237.34056Cooper, K.; Mickens, R. E. 15 2002 Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation. Zbl 1237.65095Mickens, R. E.; Gumel, Abba B. 14 2002 Numerical study of a non-standard finite-difference scheme for the van der Pol equation. Zbl 1237.65084Mickens, R. E.; Gumel, A. B. 12 2002 Step-size dependence of the period for a forward-Euler scheme of the van der Pol equation. Zbl 1237.65083Mickens, R. E. 1 2002 Mathematical and numerical study of the Duffing-harmonic oscillator. Zbl 1237.65082Mickens, R. E. 27 2001 Oscillations in an \(x^{4/3}\) potential. Zbl 1237.34044Mickens, R. E. 26 2001 A non-standard finite-difference scheme for conservative oscillators. Zbl 1237.65103Mickens, R. E. 4 2001 A nonstandard finite difference scheme for a nonlinear PDE having diffusive shock wave solutions. Zbl 0982.65095Mickens, Ronald E. 4 2001 Asymptotic solutions to a discrete Airy equation. Zbl 1005.39019Mickens, Ronald E. 3 2001 Analytical and numerical study of a non-standard finite difference scheme for the unplugged Van der pol equation. Zbl 1237.65074Mickens, R. E. 2 2001 A particular exact solution to the central core model of the renal medulla. Zbl 0999.92015Mickens, R. E. 1 2001 Nonstandard finite difference schemes. Zbl 0989.65101Mickens, Ronald E. 86 2000 Analysis of a finite-difference scheme for a linear advection-diffusion-reaction equation. Zbl 1237.76105Mickens, R. E. 19 2000 Nonstandard finite difference schemes for reaction-diffusion equations having linear advection. Zbl 0957.65081Mickens, Ronald E. 6 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 0970.00024Mickens, Ronald E. (ed.) 4 2000 Generalized harmonic oscillators. Zbl 1237.70112Mickens, Ronald E. 1 2000 An order \(\varepsilon^2\) perturbation procedure for second-order nonlinear difference equations. Zbl 0963.39005Mickens, Ronald E. 1 2000 Discretizations of nonlinear differential equations using explicit nonstandard methods. Zbl 0940.65079Mickens, Ronald E. 49 1999 Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085Mickens, Ronald E. 31 1999 Suppression of numerically induced chaos with nonstandard finite difference schemes. Zbl 0931.65079Serfaty de Markus, Alicia; Mickens, Ronald E. 9 1999 An introduction to nonstandard finite difference schemes. Zbl 1360.65007Mickens, Ronald E. 1 1999 ...and 61 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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 all top 5 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) Citations by Year Wikidata Timeline