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Existence Theorem for Abstract Measure Delay Integro-Differential Equations
S. S. Bellale,
S. B. Birajdar,
D. S. Palimkar
Issue:
Volume 4, Issue 4, August 2015
Pages:
225-231
Received:
17 May 2015
Accepted:
1 June 2015
Published:
25 June 2015
Abstract: In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the various fixed point techniques such as Schauder,s fixed point principle and Banach contraction mapping principal etc. In this paper we have proved existence and uniqueness condition for Abstract Measure delay integro-differential equations.
Abstract: In this paper, we have proved the existence and uniqueness results for an abstract measure delay integro-differential equation by using Leray-Schauder nonlinear alternative under certain Caratheodory conditions. The various aspects of the solutions of the abstract measure integro-differential equations have been studied in the literature using the ...
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Effect of Hall Current on Unsteady MHD Couette Flow and Heat Transfer of Nanofluids in a Rotating System
Ahmada Omar Ali,
Oluwole Daniel Makinde,
Yaw Nkansah-Gyekye
Issue:
Volume 4, Issue 4, August 2015
Pages:
232-244
Received:
25 May 2015
Accepted:
7 June 2015
Published:
25 June 2015
Abstract: The Hall effect on MHD Couette flow and heat transfer between two parallel plates in a rotating channel is investigated. A uniform magnetic field is applied normal to the plates and the flow is induced by the effects of Coriolis force, moving upper plate and the constant pressure gradients. Cu-water, Al2O3-water and TiO2-water nanofluids are compared for heat transfer performance. The Galerkin approximation and method of lines are employed to tackle the governing non-linear PDEs. The results show that Hall current significantly affects the flow system. The skin friction and Nusselt number profiles are presented graphically and discussed quantitatively.
Abstract: The Hall effect on MHD Couette flow and heat transfer between two parallel plates in a rotating channel is investigated. A uniform magnetic field is applied normal to the plates and the flow is induced by the effects of Coriolis force, moving upper plate and the constant pressure gradients. Cu-water, Al2O3-water and TiO2-water nanofluids are compar...
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Homotopy Method for Solving Finite Level Fuzzy Nonlinear Integral Equation
Issue:
Volume 4, Issue 4, August 2015
Pages:
245-257
Received:
23 May 2015
Accepted:
6 June 2015
Published:
29 June 2015
Abstract: In this paper, non – linear finite fuzzy Volterra integral equation of the second kind (NFVIEK2) is considered. The Homotopy analysis method will be used to solve it, and comparing with the exact solution and calculate the absolute error between them. Some numerical examples are prepared to show the efficiency and simplicity of the method.
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Population Dynamics Model for Coexistence of Three Interacting Species
M. Rafique,
M. Abdul Qader
Issue:
Volume 4, Issue 4, August 2015
Pages:
258-263
Received:
31 May 2015
Accepted:
11 June 2015
Published:
29 June 2015
Abstract: Over the years applications of mathematics in the form of mathematical modeling in a whole range of different fields including physical, social, management, biological, and medical sciences have broken all bounds. In particular, the mathematical models to study population dynamics of various interacting species in an isolated environment have attracted the attention of mathematical biologists. In nature, there may be two, three, or more species interacting within themselves giving rise to the corresponding predator-prey models. In each case, both predator and prey evolve their own strategies to deal with the situation. The parameters which influence both the predator and the pry to evoke strategies for their survival include environmental conditions, predator’s appetite, aggressiveness, liking for some particular prey, its physical fitness versus that of the prey, prey’s agility, active prudence to run away or hide, etc. In the literature interactions between, two, three or more species, sharing the same habitat have been discussed in detail. In this paper we present a model pertaining to the interaction between three species. It is a realistic model in which three species, x, y and z, interact within themselves in such a way that species y (predator) preys on species x (prey), while the species z preys on both the species x and y. Accordingly, the resulting situation has been analyzed. The objective of this paper is to analyze the possibility for three interacting species to live in an isolated environment harmoniously. The model presented here has three equilibrium points, however, only one of them has been ascertained to be locally stable. The existence of this equilibrium point signifies amicable coexistence of the three species, if no outside intervention accrues any destabilization to the existing environment.
Abstract: Over the years applications of mathematics in the form of mathematical modeling in a whole range of different fields including physical, social, management, biological, and medical sciences have broken all bounds. In particular, the mathematical models to study population dynamics of various interacting species in an isolated environment have attra...
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Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment
Okey Oseloka Onyejekwe,
Esayas Zewdie Kebede
Issue:
Volume 4, Issue 4, August 2015
Pages:
264-274
Received:
19 May 2015
Accepted:
9 June 2015
Published:
1 July 2015
Abstract: We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.
Abstract: We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while ...
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An Efficient Scheme of Differential Quadrature Based on Upwind Difference for Solving Two-dimensional Heat Transfer Problems
Abdul-Sattar Jaber Ali Al-Saif
Issue:
Volume 4, Issue 4, August 2015
Pages:
275-285
Received:
29 May 2015
Accepted:
16 June 2015
Published:
2 July 2015
Abstract: In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mechanism together with differential quadrature method to modified the numerical solutions of heat transfer problems are presented. To validate our proposed UDDQM, two convection-diffusion problems ((i) Steady-state incompressible flow problem has exact solution and (ii) Natural convection motion of the incompressible fluid flow problem hasn't exact solution) are solving numerically. Graphical results on the effects of parameter variation on velocity, temperature, Peclet number, Grashof number, and Prandtl number are presented and discussed. Numerical experiments are conducted to test its accuracy and convergence and compare it with the standard DQM and other numerical methods that are available in literature. The numerical results show the efficiency of the proposed method to handle the problems, and it is more accurate and convergent than other methods.
Abstract: In this paper, a new technique of differential quadature method called the upwind difference - differential quadature method (UDDQM) for solving two-dimensional heat transfer (convection-diffusion) problems is proposed. Also, investigated the effects of physical quantities on behavior of flow problems, and combined effects of upwind difference mech...
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The Taylor-SPH Meshfree Method: Basis and Validation
H. Idder,
M. Mabssout,
M. I. Herreros
Issue:
Volume 4, Issue 4, August 2015
Pages:
286-295
Received:
1 February 2015
Accepted:
1 February 2015
Published:
2 July 2015
Abstract: This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretization. In order to avoid numerical instabilities, two different sets of particles are used in the time discretization. To validate the Taylor-SPH method, it has been applied to solve the propagation of shock waves in elastic materials and the results have been compared with those obtained with a corrected SPH discretization combined with a 4th order Runge-Kutta time integration. The Taylor-SPH method is shown to be stable, robust and efficient and it provides more accurate results than those obtained with the standard SPH along with the Runge-Kutta time integration scheme. Numerical dispersion and diffusion are eliminated and only a reduced number of particles is required to obtain accurate results.
Abstract: This paper presents the basis and validation of the Taylor-SPH meshless method formulated in terms of stresses and velocities which can be applied to Solid Dynamic problems. The proposed method consists of applying first the time discretization by means of a Taylor series expansion in two steps and a corrected SPH method for the space discretizatio...
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Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem
Thadei Damas Sagamiko,
Nyimvua Shaban,
Cuthbert Leonard Nahonyo,
Oluwole Daniel Makinde
Issue:
Volume 4, Issue 4, August 2015
Pages:
296-312
Received:
29 June 2015
Accepted:
9 July 2015
Published:
17 July 2015
Abstract: In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations . However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge to the control of threats is studied and results indicate that increase of causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in co-existence equilibrium point.
Abstract: In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control th...
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Mathematical Modelling of the Transmission Dynamics of Ebola Virus
Amenaghawon C. Osemwinyen,
Aboubakary Diakhaby
Issue:
Volume 4, Issue 4, August 2015
Pages:
313-320
Received:
30 May 2015
Accepted:
29 June 2015
Published:
18 July 2015
Abstract: The study simulated the transmission dynamics of Ebola Zaire virus using two models: a modified SIR model with the understanding that the recovered can become infected again and the infected die at a certain rate and a quarantine model, which ascertained the effects of quarantining the infected. Furthermore, an appropriate system of Ordinary Differential Equations (ODE) was formulated for the transmission and the method of linearized stability approach was used to solve the equations. Stability analysis of both models indicated that, the Disease Free Equilibrium (DFE) states of the models were unstable if they exist. These equilibria states showed that the disease can easily be triggered off, so there is need to be constantly alert and effective preventive measures put in place against its spread. In addition, numerical experiments were carried out with the models' parameters assigned specific hypothetical values and graphs were plotted to investigate the effect of these parameters on the transmission of the disease. The results showed that, with the nature of Ebola Zaire virus, uncontrolled transmittable contacts between the infected and the susceptible can lead to a very serious outbreak with high mortality rate, since no immunity and drugs at moment. However, with effective quarantining structures put in place such situation can be better managed and outbreak controlled.
Abstract: The study simulated the transmission dynamics of Ebola Zaire virus using two models: a modified SIR model with the understanding that the recovered can become infected again and the infected die at a certain rate and a quarantine model, which ascertained the effects of quarantining the infected. Furthermore, an appropriate system of Ordinary Differ...
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Dynamical Systems and Network Flows: Traffic Flow Problem on Multi-lane Intersections (Economic Analysis)
Issue:
Volume 4, Issue 4, August 2015
Pages:
321-330
Received:
2 July 2015
Accepted:
10 July 2015
Published:
29 July 2015
Abstract: Nowadays due to rapid population growth and hence increasing demand for transportation, traffic congestion at road intersections become a serious problem for developed as well as developing countries. Traffic congestion causes considerable costs due to unproductive time losses, extra fuel consumption, accidents and also has a negative impact on the environment such as air pollution, noise and stress. Thus, economic analysis of multi-lane intersections and improvement alternatives take account of vehicles cost of fuel consumption and time costs incurred by users of the road junctions. The objective of this study was about determining average waiting time of vehicles and estimating cost incurred due to delay at unsignalized double lane roundabouts and signalized cross intersections. In this study MMAS Cellular Automata model and Poisson queuing model were used. The study tried to calculate the average waiting time (delay) of vehicles in the system (in queue plus in service) at both types of road intersections. The study was tried to quantify vehicles waiting time at both types of road intersections (cost incurred due to delay); that is cost of time lost for passengers and cost of extra fuel consumed by vehicles. Based on the findings of the study, that is based on time and fuel lost (though other factors are not included), signalized cross intersections are better than roundabouts to minimize traffic congestion problem at road junctions.
Abstract: Nowadays due to rapid population growth and hence increasing demand for transportation, traffic congestion at road intersections become a serious problem for developed as well as developing countries. Traffic congestion causes considerable costs due to unproductive time losses, extra fuel consumption, accidents and also has a negative impact on the...
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The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method
Sen-Yung Lee,
Chun-Ku Kuo
Issue:
Volume 4, Issue 4, August 2015
Pages:
331-334
Received:
23 June 2015
Accepted:
6 August 2015
Published:
14 August 2015
Abstract: The simplest equation method with the Burgers’ equation as the simplest equation is used to handle two completely integrable equations, the KdV equation and the potential KdV equation. The general forms of the multiple-soliton solutions are formally established. It is shown that the simplest equation method may provide us with a straightforward and effective mathematic tool for generating multiple-soliton solutions of nonlinear wave equations in fluid mechanics
Abstract: The simplest equation method with the Burgers’ equation as the simplest equation is used to handle two completely integrable equations, the KdV equation and the potential KdV equation. The general forms of the multiple-soliton solutions are formally established. It is shown that the simplest equation method may provide us with a straightforward and...
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