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Shooting Method (shooting + method)
Selected AbstractsThermal-diffusion and diffusion-thermo effects on convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheetINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2006A. M. Salem Abstract An analysis has been carried out to obtain the thermal-diffusion and diffusion-thermo effects on the mixed free forced convective and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheet. Here, the driving force for the flow is provided by an impermeable sheet stretched with a velocity proportional to the distance from a slit and buoyancy effects due to both temperature and concentration gradient. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically by applying the shooting method. The effects of Soret number, Dufour number, visco-elastic parameter, Porosity parameter, Grashof number and modified Grashof number on the velocity, temperature and concentration have been discussed. Numerical results for the problem considered are given and illustrated graphically. Copyright © 2006 John Wiley & Sons, Ltd. [source] Infinitely many stationary solutions for a simple climate model via a shooting methodMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2002J. I. Díaz Abstract In this paper, we study the number of steady solutions of a non-linear model arising in Climatology. By applying a shooting method we show the existence of infinitely many steady solutions for some values of a parameter (the solar constant). This method allows us to determine how many times a solution attains the critical temperature (,10°C) at which the coalbedo is assumed to be discontinuous. Copyright © 2002 John Wiley & Sons, Ltd. [source] Using switching detection and variational equations for the shooting methodOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2007Pierre Martinon Abstract We study in this paper the resolution by single shooting of an optimal control problem with a bang-bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright © 2007 John Wiley & Sons, Ltd. [source] Trajectory optimization involving sloshing mediaOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2002Harald Leonpacher Abstract This paper is concerned with the optimization of the transport motion of an open topped fluid filled container within a warehouse environment. In particular, optimal trajectories of the motion of the driver,container system in two-dimensional space will be investigated via numerical solutions of the model equations using sequential quadratic programming. The fluid and the mechanical facility that moves the container are subject to several constraints. The objective of the optimization is the time to transport the container from an initial position to its final destination within the warehouse. Optimization criteria are investigated to control the movement of the fluid within the container. The systems of ordinary and partial differential equations, representing the dynamics of the models are solved numerically using a direct shooting method. The resulting non-linear programming problem is solved using sequential quadratic programming (SQP). Copyright © 2002 John Wiley & Sons, Ltd. [source] Optimal and sub-optimal control in Dengue epidemicsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2001Marco Antonio Leonel Caetano Abstract This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright © 2001 John Wiley & Sons, Ltd. [source] Effect of a Magnetic Field on a Micropolar Fluid Flow in the Vicinity of an Axisymmetric Stagnation Point on a Circular CylinderCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 8 2009G. M. Abdel-Rahman Abstract The effect of a magnetic field on a micropolar fluid flow in the vicinity of an axisymmetric stagnation point on a circular cylinder is studied numerically. The governing conservation equations of continuity, momentum and angular momentum are partial differential equations which are transformed into a system of ordinary differential equations by using the usual similarity transformations. The resulting system of coupled non-linear ordinary differential equations is solved numerically by using the shooting method. The numerical results indicate the velocity, angular velocity and pressure distributions for different parameters of the problem including Reynolds number, magnetic parameter and dimensionless material properties, etc. In addition, the effect of the pertinent parameters on the local skin friction coefficient and the couple stress are discussed numerically and illustrated graphically. [source] | ||||||||||