Abstract: The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.
Abstract: In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.
Abstract: This paper deals with the theoretical and numerical
investigation of magneto hydrodynamic boundary layer flow of a
nanofluid past a wedge shaped wick in heat pipe used for the cooling
of electronic components and different type of machines. To
incorporate the effect of nanoparticle diameter, concentration of
nanoparticles in the pure fluid, nanothermal layer formed around the
nanoparticle and Brownian motion of nanoparticles etc., appropriate
models are used for the effective thermal and physical properties of
nanofluids. To model the rotation of nanoparticles inside the base
fluid, microfluidics theory is used. In this investigation ethylene
glycol (EG) based nanofluids, are taken into account. The non-linear
equations governing the flow and heat transfer are solved by using a
very effective particle swarm optimization technique along with
Runge-Kutta method. The values of heat transfer coefficient are
found for different parameters involved in the formulation viz.
nanoparticle concentration, nanoparticle size, magnetic field and
wedge angle etc. It is found that, the wedge angle, presence of
magnetic field, nanoparticle size and nanoparticle concentration etc.
have prominent effects on fluid flow and heat transfer characteristics
for the considered configuration.
Abstract: The flexible follower response of a translating cam with
four different profiles for rise-dwell-fall-dwell (RDFD) motion is
investigated. The cycloidal displacement motion, the modified
sinusoidal acceleration motion, the modified trapezoidal acceleration
motion, and the 3-4-5 polynomial motion are employed to describe the
rise and the fall motions of the follower and the associated four kinds of
cam profiles are studied. Since the follower flexibility is considered,
the contact point of the roller and the cam is an unknown. Two
geometric constraints formulated to restrain the unknown position are
substituted into Hamilton-s principle with Lagrange multipliers.
Applying the assumed mode method, one can obtain the governing
equations of motion as non-linear differential-algebraic equations. The
equations are solved using Runge-Kutta method. Then, the responses of
the flexible follower undergoing the four different motions are
investigated in time domain and in frequency domain.
Abstract: In this paper a new embedded Singly Diagonally
Implicit Runge-Kutta Nystrom fourth order in fifth order method for
solving special second order initial value problems is derived. A
standard set of test problems are tested upon and comparisons on the
numerical results are made when the same set of test problems are
reduced to first order systems and solved using the existing
embedded diagonally implicit Runge-Kutta method. The results
suggests the superiority of the new method.
Abstract: In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Abstract: The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.