Department of Mathematics

      University of Dayton

Muhammad Usman, Ph.D.Dr. Usman
Associate Professor of Mathematics
(On sabbatical leave for Fall 2014)


Ph.D. (Mathematics) University of Cincinnati, 2007
M.S.   (Nuclear Engg.) University of Cincinnati, 2007
M.S.   (Mathematics) Ohio University, 2001
M.A.   (Biophysics) Ohio University, 2001
300 College Park,

Dayton, OH 45469-2316, USA

Office Science Center 103 C
Phone 937-229-2101
Fax 937-229-2566

Schedule | Research Interests  | Computer Skills  | Publications | Professional Activities | Teaching| Links | Student Mentoring

Research Interests

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

AMS Classification

Computer Skills

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

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) (Impact factor 0.263)
  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. (Impact factor 0.607)
  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) (Impact factor 1.005)
  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) (Impact factor 1.383)
  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. (Impact factor 1.144)
  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) (Impact factor 1.454)
  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) (Impact factor 1.093)
  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.(Impact factor 0.74)
  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 Modelling, Volume 36, Issue 2(2012), 736--742. (Impact factor 1.706)
  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 here)
  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. (Impact factor 0.461)
  17. With M. Imran, A Generalization of Poincare-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System, Appear in Dynamics of Continuous, Discrete Impulsive Systems Series A: Mathematical Analysis, (21) 2014, 111--134.
  18. With Giacomo Flora*, A Numerical Study of In Vitro Inhibition of Mutation of Cancer Cells Using Two Different Methods (in progress)
  19. With Christopher  Yakopcic*, Stability Analysis of a Model for In Vitro Inhibition of Cancer Cell Mutation (in progress)
  20. With Nicholas Haynes*, Numerical Study of eventual periodicity of forced oscillations of a Class of Nonlinear Dispersive Wave Equation (in progress)

* Graduate Students


Professional Activities

Referee Work For Journals 

Mathematics With Computer Applications, Applications and Applied Mathematics, International Journal of Computer Mathematics, World Applied Sciences Journal, Zeitschrift f�r Naturforschung A (A Journal of Physical Sciences), Mathematical and Computer Modelling, 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, Nonlinear Dynamics, Abstract and Applied Analysis.

Teaching (On Sabbatical Leave in Fall 2014)

For previous teaching click here

Useful Links

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