Muhammad Usman

Contact Information

Muhammad Usman

Associate Professor

  • Full-Time Faculty


  • Ph.D., University of Cincinnati, 2007
  • M.S., University of Cincinnati, 2007, Nuclear Engineering
  • M.S., Ohio University, 2001, Mathematics
  • M.A., Ohio University, 2001, Biophysics
  • M. Phil. Quaid-I-Azam University, 1996 (Analytical Mechanics)
  • B.S., Quaid-I-Azam University, 1994

Professional Activities

Referee Work for Journals:

Mathematics With Computer Applications, Applications and Applied Mathematics, International Journal of Computer Mathematics, World Applied Sciences Journal, Zeitschrift für Naturforschung A (A Journal of Physical Sciences), Mathematical and Computer Modeling, Applied Mathematics and Computation, Engineering Computations, Progresses in Computational Fluid Dynamics, International Journal of Physical Sciences, Applied Mathematics Letters A, The Open Mathematics Journal, International Journal for Numerical Methods for Heat and Fluid Flow, Journal Of King Saud University-Science, Electronic Journal of Qualitative Theory of Differential Equations, Communications in Mathematical Analysis, Asia-Pacific Journal of Chemical Engineering, Reviewer for Mathematical Reviews, Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM) of European Society of Computational Methods in Sciences and Engineering (ESCMSE), ASME 2013, International Mechanical Engineering Congress and Exposition, Abstract and Applied Analysis, Physics Letters A, Applied Mathematics and Information Sciences, Nonlinear Analysis: Modeling and Control, Advances in Mathematical Physics, Applied Mathematical Modeling

Research Interests

  • Numerical Analysis
  • Mathematical Biology
  • Nonlinear PDEs and Applications
  • Scientific Computing
  • Analytical Mechanics

Selected Publications

  1. With Bingyu Zhang, "Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability," Springer, Journal of Systems Science and Complexity, Vol. 20, No.2, p 284-292, June 2007. (Citations)
  2. With Miriam Poteet*, "Stability of Steady State Solutions of the Forced Kuramoto-Sivashinsky (KS) Equation," Advances in Differential Equations and Control Processes, Vol. 4, Issue 2, p 119-131, 2009.
  3. With Bingyu Zhang, "Forced Oscillations of the Korteweg-de Vries Equation on a Bounded Domain and their Stability," Discrete and Continuous Dynamical Systems-Series A, Vol. 26, No.4, p 1509-1523, 2010. (Citations)
  4. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, Sefa Anil Sezer, "Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Pade' Approximation," Mathematical Problems in Engineering, Volume 2010 (2010), Article ID 318298, doi:10.1155/2010/318298 (Citations)
  5. With Syed Tauseef Mohyud-Din, M. M. Hosseini, H. Ghaneai, "Auxiliary Parameter in the Variational Iteration Method and its Optimal Determination," International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 11, No. 7, July 2010, Pages 495-501.
  6. With Sirajul Haq, Nagina Bibi, S.I.A. Tirmizi, "Meshless method of lines for the numerical solution of generalized Kuramoto-Shivashinsky equation," Applied Mathematics and Computation, Volume 217, Issue 6, 15 November 2010, Pages 2404-2413. (Citations)
  7. With Elham Negahdary*, Syed Tauseef Mohyud-Din, "A meshless numerical solution of the family of generalized fifth-order Korteweg-de Vries equations," International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 22, Issue 5, 2012. (Citations)
  8. With Bingyu Zhang and Ivonne Rivas, "Global well-posedness and asymptotic behavior of a class of initial-boundary-value problems of the KdV equation on a finite domain," Mathematical Control and Related Fields, Volume 1, Issue 1: 61-81, 2011.(Citations)
  9. With Rahmat Ali Khan, "Long Time Dynamics of Forced Oscillations of the Korteweg-de Vries Equation Using Homotopy Perturbation Method," Studies in Nonliear Sciences, 1(3): 57-62, 2010.
  10. With Paul Eloe, "Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation," Nonlinear Studies, The International Journal, Vol.19(2), 2012, pp 215-224.
  11. With Jian Gao* and Syed Tauseef Mohyud-Din, "Numerical Solution of Heat Propagation in Living Tissue Using Method of Lines," Nonlinear Science Letters C: Nano, Biology and Environment, Vol. 1, No. 1, 2011, 15-20.
  12. With Paul Eloe, "Fully Nonlinear Boundary Value Problems with Impulse," E. J. Qualitative Theory of Diff. Equ., No. 21 (2011), pp. 1-11. (Citations)
  13. With Rahmat Ali Khan, "Eventual Periodicity of Forced Oscillations of Korteweg-de Vries Type Equation," Applied Mathematical Modeling, Volume 36, Issue 2(2012), 736-742.
  14. With Amit Singh, "A New Undergraduate Curriculum on Mathematical Biology at University of Dayton," Journal of STEM Education: Innovation and Research, Volume 12. Issue 5 & 6 (2011), 58-66.
  15. With Giacomo Flora*, "FALSKAN: A GUI Interface for the Numerical Solution of the Falkner-Skan Problem," Journal of Pure and Applied Mathematics: Advances and Applications, Vol. 8(1), (2012), 11-24. Download all MATLAB codes >>
  16. With Rahmat Ali Khan, "A study of the GAM approach to solve laminar boundary layer equations in the presence of a wedge," Applied Mathematical Sciences, Vol. 6, No. 117-120, (2012), 5947-5958.
  17. Muhammad Usman, M. Imran, A Generalization of Poincare-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System, Dynamics of Continuous, Discrete Impulsive Systems Series A: Mathematical Analysis, Vol. 21, Issue 1, (2014), 111--134.
  18. Ambreen Afsar Khan, R Ellahi, M Usman, The effects of variable viscosity on the peristaltic flow of non-Newtonian fluid through a porous medium in an inclined channel with slip boundary conditions, Journal of Porous Media, 16(1), pp 59--67, 2013. (Citations) (Impact factor 0.467) (Download)
  19. Yasir Khan, Muhammad Usman, Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems,International Journal of Nonlinear Sciences and Numerical Simulation, 15(1), pp 19--25, 2014. (Impact factor 0.453)
  20. Muhammad Usman, Abdallah Shaaban, A transformation to convert a mathematical model of radiation capacity of a river containing little drift into a modified Bessel equation of Order zero. (Submitted)
  21. Chen, J., Dai, W., Usman, M. An Accurate Compact Finite Difference Scheme with Absorbing Boundary Condition for Solving the Forced KdV Equation. (Submitted)
  22. Usman, M., Haynes, N., Al-Khaled, K., Schiesser, W. A numerical study of eventual periodicity of the Korteweg-de Vries type equation using sinc collocation method. Volume 330, 1 March 2018, Pages 417-428. IF 1.357
  23. Dur-e-Ahmad Muhammad, Usman Muhammad, Khan Adnan and Imran Mudassar, Optimal Control Analysis of Ebola Disease with Control Strategies of Quarantine and Vaccination, Infectious Diseases of Poverty, 2016, 5:72, DOI: 10.1186/s40249-016-0161-6
  24. Muhammad Usman, Giacomo Flora, Chris Yakopcic, Mudassar Imran, A Computational Study and Stability Analysis of a MathematicalModel for In Vitro Inhibition of Cancer Cell Mutation, Int. J. Appl. Comput. Math, 2016, DOI 10.1007/s40819-016-0201- 
  25. A mathematical model for transmission dynamics of Zika fever, Mudassar Imran, Muhammad Usman, Adnan Khan, Muhammad Dur-e-Ahmad, Differential Equations and Dynamical Systems (DEDS).
  26. A Study of Bifurcation Parameters in Travelling Wave Solution of a Damped Forced Korteweg-de Vries-Kuramoto Sivashinsky Type Equation, M. Imran, Y. Raffoul, M. Usman, C. Zhang, DISCRETE AND CONTINUOUS doi:10.3934/dcdss.2018043, DYNAMICAL SYSTEMS SERIES S Volume 11, Number 4, August 2018 pp. 691–705, IF 0.78
  27. Iftikhar Ahmad, Muhammad Usman, Hina Zahid, Muhammad Bilal, Stochastic technique for solutions of nonlinear Fin equation arising in thermal equilibrium model (accepted)

* Graduate Student

Computing Experience

Visual Basic, Fortran, C/C++, MATLAB, Mathematica, Maple, COBOL, Linux, Parallel Computing with MPI, PVM, Latex