Department of Mathematics

      University of Dayton

Muhammad Usman, Ph.D.Dr. Usman
Associate Professor of Mathematics

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 (My Erdos number is 3)

  1. Muhammad Usman,  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 0.370)
  2. Miriam Poteet*, Muhammad Usman, 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. Muhammad Usman,  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 0.923)

  4. Sirajul Haq, Nagina Bibi, S.I.A. Tirmizi, M. Usman, 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 1.60)

  5. Syed Tauseef Mohyud-Din, Elham Negahdary*, Muhammad Usman, 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 0.919)

  6. Ivonne Rivas, Muhammad Usman, Bingyu Zhang, 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) (Impact factor 1.095)

  7. Rahmat Ali Khan, Muhammad Usman,  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.

  8. Paul Eloe, Muhammad Usman, 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)

  9. Jian Gao*, Syed Tauseef Mohyud-Din, Muhammad Usman 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.

  10. Paul Eloe, Muhammad Usman Fully Nonlinear Boundary Value Problems with Impulse, E. J. Qualitative Theory of Diff. Equ., No. 21 (2011), pp. 1-11. (Citations) (Impact factor 0.719)

  11. Rahmat Ali Khan, Muhammad UsmanEventual Periodicity of Forced Oscillations of Korteweg-de Vries Type Equation, Applied Mathematical Modelling, Volume 36, Issue 2(2012), 736--742. (Impact factor 1.706) (Citations)

  12. Muhammad Usman, 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. (Citations)

  13. Giacomo Flora*, Muhammad Usman, 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)

  14. Rahmat Ali Khan, Muhammad Usman, 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)

  15. 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.

  16. 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)

  17. 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)

  18.  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) 

  19. Chen, J., Dai, W., Usman, M. An Accurate Compact Finite Difference Scheme with Absorbing Boundary Condition for Solving the Forced KdV Equation. (Submitted)

  20. 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. (Submitted)

* 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 fr 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, Canadian Journal of Physics, Nonlinear Dynamics, Rose-Hulman Undergraduate Mathematics Journal.

Teaching (Fall 2015)

MTH 218-03 (Analytical Geometry & Calculus III)

MTH 218-06 (Analytical Geometry & Calculus III)

MTH 555 (Numerical Analysis I)

For previous teaching click here

Useful Links

LaTeX Resources for Students

My preferences on freeware

UD Links:

Transpositional Relation Geometrical View