Abstract:
This
paper investigates the effect of inflow, outflow and shock waves in a single lane
highway traffic flow problem. A constant source term has been introduced to demonstrate
the inflow and outflow. The classical Lighthill Whitham and Richards (LWR) model
combined with the Greenshields model is used to obtain analytical and numerical
solutions. The model is treated as an IBVP and numerical solutions are presented
using Lax Friedrichs scheme. Godunov method is also used to present shock wave analysis.
The numerical procedures adopted in this investigation yield results which are very
much consistent with real life scenario in terms of traffic density and velocity.

Korteweg de-Vries (K-dV) has wide applications in physics, engineering and fluid mechanics. In this the Korteweg de-Vries equation with traveling solitary waves and numerical estimation of analytic solutions have been studied. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by PANG, BIAN and CHAO. We have solved the set of exact traveling wave solution analytically. Some numerical results of time dependent wave solutions have been presented graphically and discussed. This procedure has a potential to be used in more complex system of many types of K-dV equation.

All solutions of the Korteweg-de Vries(K-dV) equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi) periodic. The development of numerical techniques for obtaining approximate solution of partial differential equations has very much increased in the finite element and finite difference methods. Recently, new auxiliary equation method introduced by PANG, BIAN and CHAO is applied to the analytical solution of K-dV equation and wavelet methods are applied to the numerical solution of partial differential equations. Pioneer works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others. In this research we employ the new auxiliary equation method to obtain the effect of dispersion term on travelling wave solution of K-dV and their numerical estimation as well. Our approach views the limit behavior as an invariant measure of the fast motion drifted by the slow component, where the known constants of motion of the fast system are employed as slowly evolv- ing observables; averaging equations for the latter lead to computation of the characteristic features of the motion.

Abstract:
In this paper, the age-specific population of Bangladesh based on a linear first order (hyperbolic) partial differential equation which is known as Von-Foerster Equation is studied. Applying quadratic polynomial curve fitting, the total population and population density of Bangladesh are projected for the years 2001 to 2050 based on the explicit upwind finite difference scheme for the age-structured population model based on given data (source: BBS & ICDDR, B) for initial value in the year 2001. For each age-group, the future birth rates and death rates are estimated by using quadratic polynomial curve fitting of the data for the years 2001 to 2012. Quadratic polynomial curve fitting is also used for the boundary value as the (0 - 4) age-group population based on the population size of the age-group for the years 2001 to 2012.

Abstract:
In the history of option pricing, Black-Scholes model is one of the most significant models. In this article, the main concern is the numerical solution of the Black-Scholes model (a.k.a. Black/Scholes/Merton) for the European call option in a different way. The model is described and an explicit difference scheme was used for the numerical approximation. The stability condition of the scheme is established through convex combination. A different way was used to obtain the numerical value of the model. Estimation of the relative error was calculated in L1-norm in order to test the accuracy of the scheme. Finally, a comparison of the numerical outcomes with the value obtained by another scheme is given.

Abstract:
The conjugate effects of radiation and joule heating on magnetohydrodynamic (MHD) free convection flow along a sphere with heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton’s linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically for some selected values of parameters set consisting of heat generation parameter Q, radiation parameter Rd, magnetic parameter M, joule heating parameter J and the Prandtl number Pr.

Abstract:
A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich’s scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.

Abstract:
The
group-theorytic approach is applied for solving the problem of the unsteady MHD
mixed convective flow past on a moving curved surface. The application of
two-parameter groups reduces the number of independent variables by two, and
consequently the system of governing partial differential equations with boundary
conditions reduces to a system of ordinary differential equations with
appropriate boundary conditions. The obtained ordinary differential equations
are solved numerically using the shooting method. The effects of varying
parameters governing the problem are studied. A comparison with previous work
is presented.

The effect of external magnetic field and internal heat generation or absorption on a steady two-dimensional natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for velocity, temperature, skin friction, the rate of heat transfer are obtained for different values of the selected parameters, such as viscous dissipation parameter (Vd), heat generation parameter (Q), magnetic parameter (M) and presented graphically and discussed. Streamlines and isotherms are presented for selected values of heat generation parameter and explained.

Abstract:
In this study, we applied a new algorithm based on Homotopy Perturbation Method (HPM) to evaluate the temperature distribution of a straight rectangular fin with temperature dependent surface heat flux for all possible types of heat transfer. The local heat transfer coefficient is considered to vary with a power-law function of temperature. The time interval is divided into several subintervals and the HPM solutions are applied successively over these reduced time intervals. Comparisons between the 13-term Adomian decomposition solution and 6-term modified HPM solution are made. Comparison of the results obtained by modified HPM with that obtained by the Adomian Decomposition Method (ADM) reveals that the obtained modified HPM solution is quite accurate when only the six terms are used in the series expansion.