Research

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. 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)

3. Sirajul Haq, Nagina Bibi, S.I.A. Tirmizi, M. Usman, Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation, Applied Mathematics and Computation, Volume 217, Issue 6, 15 November 2010, Pages 2404-2413. (Citations) . (Impact factor 1.60)

4. 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)

5. 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)

6. Rahmat Ali Khan, Muhammad Usman, Long Time Dynamics of Forced Oscillations of the Korteweg-de Vries Equation Using Homotopy Perturbation Method, Studies in Nonlinear Sciences, 1(3): 57--62, 2010.

7. 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)

8. 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.

9. 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)

10. Rahmat Ali Khan, Muhammad Usman, 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). (Citations)

11. 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)

12. 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)

13. 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)

14. 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.

15. 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)

16. 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 0.89)

17. 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) 

18. 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. Journal of Computational and Applied Mathematics,  330 (2018) 417–428 . IF 1.357

19. 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 IF 4.11, 5:72, 2016, 5:72, DOI: 10.1186/s40249-016-0161-6

20. Muhammad Usman, Giacomo Flora*, Chris Yakopcic*, Mudassar Imran, A Computational Study and Stability Analysis of a Mathematical Model for In Vitro Inhibition of Cancer Cell Mutation,  Int. J. Appl. Comput. Math,   September 2017, Volume 3, Issue 3, pp 1861–1878

21. 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), p1-24, 2017.

22. M. Imran, Y. Raffoul, M. Usman, C. Zhang*, A Study of Bifurcation Parameters in Travelling Wave Solution of a Damped Forced Korteweg-de Vries-Kuramoto Sivashinsky Type Equation, DCDS Series S, Pages: 691 - 705, Volume 11, Issue 4, August 2018.       doi:10.3934/dcdss.2018043,  IF 0.78

23. Marjan Uddin, Kamran Kamran, Muhammad Usman, Amjad Ali, On The Laplace Transformed Based Local Meshless Method For Fractional Order Diffusion Order Equation, International Journal for Computational Methods in Engineering Science & Mechanics, Vol 0, No.0 1--5, 2018.

24. Mudassar Imran, Muhammad Usman, Tufail Malik, and Ali R. Ansari, Mathematical analysis of the role of hospitalization/isolation in controlling the spread of Zika fever, Virus Research, Vol. 255, pages 95-104, 2018. https://doi.org/10.1016/j.virusres.2018.07.002

25. K. Ramesh, N. S. Akbar,  M. Usman, Biomechanically driven flow of a magnetohydrodynamic bio-fluid in a micro-vessel with slip and convective boundary conditions, Microsystem Technologies, p-1-23, 2018, Springer, https://doi.org/10.1007/s00542-018-3945-8(0123456789().,-volV)(0123456789().,-volV) IF 1.195

26.  Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman, Stochastic technique for solutions of nonlinear fin equation arising in thermal equilibrium, Thermal Science, International Scientific Journal, https://doi.org/10.2298/TSCI180221057A

27.  Marjan Uddin, Hameed Ullah Jan and Muhammad Usman, RBF-FD Method For Some Dispersive Wave Equations and Their Eventual Periodicity, Computer Modeling in Engineering & Sciences, vol.123, no.2, pp.797-819, 2020.

28. Xiaofeng Wang, Weizhong Dai, Muhammad Usman, A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing,  Applied Numerical Mathematics, Volume 160, February 2021, Pages 102-121

29. Muhammad Usman, Shaaban Abdallah, Mudassar Imran, Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using Asymptotic Perturbation Method, Math. Comput. Appl. 2021, 26(2), 33; https://doi.org/10.3390/mca26020033

30. Iftikhar Ahmad, Syed Ibrar Hussain, Muhammad Usman, Hira Ilyas, On the Solutions of Zabolotskaya-Khokhlov and Diffusion of Oxygen Equations Using a Sinc Collocation Method, Partial Differential Equations in Applied Mathematics, Vol. 4, July 2021.

31. Muhammad Usman, Marjan Uddin, Anup Lamichhane, Sajjad Hussain Shah, Meshless Method of Approximate Particular Solution for an Initial Boundary Value Problem of the Korteweg-de Vries Equation Type Equation and Eventual Periodicity, Partial Differential Equations in Applied Mathematics, Vol 4, 2021, https://doi.org/10.1016/j.padiff.2021.100088 

32.  Marjan Uddin, Hameed Ullah Jan, Muhammad Usman, RBF-PS method for approximation and eventual periodicity of fractional and integer type KdV equations, Partial Differential Equations in Applied Mathematics, Vol. 5, June 2022, 100288, https://doi.org/10.1016/j.padiff.2022.100288

33. Marjan Uddin, Hameed Ullah Jan, Muhammad Usman, "On the Solution of Fractional Order KdV Equation and Its Periodicity on Bounded Domain Using Radial Basis Functions", Mathematical Problems in Engineering, vol. 2022, Article ID 8924450, 10 pages, 2022. https://doi.org/10.1155/2022/8924450

* denotes a graduate student

Colloquium/Talks

1. A collocation method for a class of a nonlinear partial differential equation, The Eleventh IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory,  Athens, GA, USA, April 17-19, 2019.

2. Nonlinear and Stability Analysis for a Ship with a General Roll-damping Model Using An Asymptotic Perturbation Method, American Institute of Mathematical Sciences (AIMS) International conference series on Dynamical Systems and Differential Equations,  Taipei Taiwan, July 5-10, 2018.

3. Theory and Computation: Forced Oscillations of a Class of Shallow Water Wave Equation, Mathematical Biology and Dynamical Systems Seminar,  Ohio University, Athens, OH, April 03, 2018.

4. Usman, M., Sigma-Xi Interdisciplinary Seminar 2017-18, Feb. 16, 2018, Shallow water wave models; Solitons and Applications.

5. Usman, M., International Symposium on Biology and Ecology; Education and Research (BEER 2017) at Illinois State University Normal, IL, October 6--8, 2017, KEEN in Differential Equations and Entrepreneurial Mindset.

6. Usman, M., Invited Talk, AMMCS-2017 International Conference: Applied Mathematics, Modeling and Computational Science Conference August 20 - 25, 2017, Wilfrid Laurier University, Canada, Computational Study of Eventual Periodicity of Forced Oscillations of an Initial-Boundary-Value Problem of the KdV Type Equation.

7. Usman, M., Invited Talk at The 10th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, March 29-April 01, 2017, University of Georgia, Athen, GA, A Study of Bifurcation Parameters in Travelling Wave Solutions of a Damped Forced Korteweg de Vries-Kuramoto Sivashinsky Type Equation.

8. Poster Presentation at the Celebration of Sciences at the University of Dayton. October 11, 2016, (Poster) 

9. Usman, M., Invited Lecture, The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL, USA, "Bifurcations in traveling wave solutions of the Kuramoto Sivashinsky type perturbed forced equation". (July 2, 2016).

10. Usman, M., Invited Lecture, Seminar on Mathematical Tools for Option Pricing, College of Business and Commerce, University of Gujrat, Pakistan, Sponsored by the Government of Pakistan and University of Gujrat, Pakistan. (January 12, 2016).

11. Usman, M., Invited Lecture, Seminar on Bifurcation analysis of some nonlinear dispersive wave equations, Sponsored by the Government of Pakistan and University of Gujrat, Pakistan. (January 8, 2016).

12. Usman, M., Invited Lecture, Seminar on computational study of forced oscillations of a Korteweg-de Vries type equation, Sponsored by the Government of Pakistan and University of Gujrat, Pakistan. (January 7, 2016).

13. Usman, M., Invited Lecture, Seminar on Some analysis results on a family of nonlinear dispersive wave equations, Sponsored by Government of Pakistan and University of Gujrat, Pakistan. (January 6, 2016).

14. Usman, M., Invited Lecture, Seminar on A history and discovery of equation for nonlinear shallow water waves, Sponsored by the Government of Pakistan and University of Gujrat, University of Gujrat, Pakistan. (January 5, 2016).

15. Usman, M., Invited Lecture, Seminar for General Audience on Some Applications of Computational Mathematics in STEM Disciplines at the University of Gujrat, Pakistan, Sponsored by the Government of Pakistan and University of Gujrat. (January 4, 2016).

16. Usman, M., Workshop, Delivered a National Workshop on Computational Methods in Engineering and Finance, Sponsored by Government of Pakistan, University of Gujrat, Pakistan. (January 1, 2016).

17. October 2, 2015, Invited talk at the Wright State University Colloquium, Theoretical and recent computational results on the forced oscillations of a Korteweg-de Vries equation.

18. Invited Talk, A perturbation method to study the stability of travelling wave solutions of a class of nonlinear partial differential equations. Fall Southeastern Sectional Meeting of American Mathematical Society, University of Memphis, Memphis, TN, October 17-18, 2015 (Saturday - Sunday)

• Service to Profession:
  Co-Editor of a special issue of Discrete and Continuous Dynamical System Series S (AIMS Journal) Chaudry Masood Khalique, Muhammad Usman, Maria Luz Gandarais. Nonlinear differential equations: Lie symmetries, conservation laws and other approaches of solving. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : i-ii. doi: 10.3934/dcdss.2020415,  https://www.aimsciences.org/article/doi/10.3934/dcdss.2020415

• Co-Editor of a special issue of Abstract and Applied Analysis

Analytical and Numerical Approaches for Complicated Nonlinear Equations.