Muhammad Usman, Ph.D.                                                       

         Assistant Professor, 2007

        Ph.D. (Mathematics) University of Cincinnati, 2007

        M.S. (Nuclear Engg.) University of Cincinnati, 2007

        M.S. (Mathematics) Ohio University, 2001

        M.A. (Physics) Ohio University, 2001

 

        Contact Information:

          Science Center 103-C

Muhammad.Usman@udayton.edu

           (937) 229-2101

 

 

Research Interests

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

 

Teaching

           

 

 

 

Student Activities

To see my students' Stander Symposium posters click here

 

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.
  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.
  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
  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.
  7. With Elham Negahdary*, Syed Tauseef Mohyud-Din, A meshless numerical solution of the family of generalized fifth-order Korteweg-de Vries equations (to appear in International Journal of Numerical Methods for Heat and Fluid Flow)
  8. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, An Iterative Algorithm for Nonlinear BVPs Using Pade´ Approximants, World Applied Sciences Journal, 10(6): 637--644, 2010.
  9. 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.
  10. 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.
  11. With Paul Eloe, Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation (to appear in issue 2, 2012 of Nonlinear Studies, The International Journal)
  12. 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.
  13. With Paul Eloe, Fully Nonlinear Boundary Value Problems with Impulse, E. J. Qualitative Theory of Diff. Equ., No. 21 (2011), pp. 1-11.
  14. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, Homotopy analysis method for fractional partial differential equations, International Journal of the Physical Sciences Vol. 6(1),  4 January, 2011, pp. 136-145.
  15. 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.

  16. 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.

  17. With Giacomo Flora* and Syed Tauseef Mohyud-Din, FALSKAN: A GUI Interface for the Numerical Solution of the Falkner-Skan Problem (under review)

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* Publications with graduate students