A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal ControlRead the full article
Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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An Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequality
This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff-type variational inequality are derived.
Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment
Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, , is computed using the next generation matrix method. The results show that if , the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.
Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method
In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, . These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.
Approximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equations
In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.
Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids
In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.
Solving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Time
In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.