Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

External Link

Muhammad Usman

Selected Works

2015

Articles 1 - 5 of 5

Full-Text Articles in Physical Sciences and Mathematics

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh Mar 2015

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Muhammad Usman

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

Go to article

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Khan, Muhammad Usman Mar 2015

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Khan, Muhammad Usman

Muhammad Usman

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.

Go to article

Forced Oscillations Of A Class Of Nonlinear Dispersive Wave Equations And Their Stability, Muhammad Usman, Bingyu Zhang Mar 2015

Forced Oscillations Of A Class Of Nonlinear Dispersive Wave Equations And Their Stability, Muhammad Usman, Bingyu Zhang

Muhammad Usman

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a finite domain. Consideration is given to the initial-boundary-value problem * {ut+ux=uux+u(0,t)=h(t),uxxx=0,u(x,0)=ϕ(x),u(1,t)=0,ux(1,t)=0,00,t>0. It is shown that if the boundary …

Go to article

Modified Homotopy Perturbation Transform Method: A Paradigm For Nonlinear Boundary Layer Problems, Yasir Khan, Muhammad Usman Mar 2015

Modified Homotopy Perturbation Transform Method: A Paradigm For Nonlinear Boundary Layer Problems, Yasir Khan, Muhammad Usman

Muhammad Usman

This paper suggests a novel modified homotopy perturbation transform method (MHPTM) for a nonlinear boundary layer problem by suitable choice of an initial solution. The steady Navier–Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The governing nonlinear differential equations are solved by means of MHPTM. The equations are Laplace transformed and the nonlinear terms represented by He's polynomials. The series solution of the nonlinear boundary layer problem is obtained. For such a boundary layer problem, the second derivative at zero is an important point of function, so we have computed f″(0) and compared it …

Go to article

Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman Mar 2015

Bifurcations In Steady State Solutions Of A Class Of Nonlinear Dispersive Wave Equation, Paul Eloe, Muhammad Usman

Muhammad Usman

We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.

Go to article