This paper addresses the problem of finding the trajectory, for a glider, that maximizes the final velocity and respect both initial and terminal conditions on the state. A new set of differential equations governing the system, deduced using optimal control theory, is proposed. To solve this system of equations, an algorithm based on an indirect shooting method is described. It provides paths ...

Abstract—A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using th...

Border collision bifurcations refer to situations where a small parameter variation induces a change in the event sequence of a hybrid system. At such a bifurcation, the system trajectory makes tangential contact with an event triggering hypersurface. This bounding case separates regions of (generally) quite different dynamic behaviour. In the paper, the conditions governing bifurcation points ...

This paper presents a novel shooting algorithm for solving two-point boundary value problems (BVPs) for differential equations of one independent variable. This algorithm includes the following steps: First, a shooting step is performed, in which a guess for the initial condition is made and a forward numerical integration of the differential equation is performed so that an Initial Value Probl...

We establish the existence of the viscous proole of an undriven divergent detonation wave for a model problem with small viscosity. It is known that there is a sonic point inside the reaction zone of a divergent detonation wave. As a consequence, the detonation wave proole is a transonic proole and the wave speed cannot be determined before the problem is solved. The wave speed may be interpret...

Within the last decade, there has been growing interest in the study of multiple solutions of twoand multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective to...

In this paper, the problem of unsteady stagnationpoint flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer c...

Abstract. In the present study, an analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperature-dependent viscosity and thermal radiation on an unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate. The governing nonlinear par...

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial splinefunction-based method combined with shooting method is considered to find approximate solution for a class of fract...

The practical applicability of optimal solutions of control problems substantially depends upon the availability of feedback control schemes to compensate for unavoidable disturbances. Three numerical methods of treating these schemes are presented and discussed in this paper. They can be applied to a rather general class of optimal control problems (for example, problems with inequality constr...