Muhammad Usman

Associate Professor
Full-Time Faculty
College of Arts and Sciences: Mathematics

Degrees

  • 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
  • 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. With Giacomo Flora*, "A Numerical Study of In Vitro Inhibition of Mutation of Cancer Cells Using Two Different Methods." (in progress)
  18. With Christopher Yakopcic*, "Stability Analysis of a Model for In Vitro Inhibition of Cancer Cell Mutation." (in progress)
  19. With Nicholas Haynes*, "Numerical Study of eventual periodicity of forced oscillations of a Class of Nonlinear Dispersive Wave Equation." (in progress)

* Graduate Student

Computing Experience

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