We propose a Hamilton-Jacobi equation approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton-Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins’ and Reeds-Shepp’s cars, and gives further generalizations. We show that the value function of the control problem so...

We consider the single-leg airline revenue management problem in continuous time with Poisson arrivals. Earlier work on this problem generally uses the Hamilton-Jacobi-Bellman equation to find an optimal policy whenever the value function is differentiable and is a solution to this equation. In this paper, we employ a different probabilistic approach, which do not rely on the smoothness of the ...

A canonical problem in real option pricing, as described in the classic text of Dixit and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic cashflow. In this paper we are interested in this problem in an incomplete market where the cashflow is not spanned by the traded assets. We follow the formulation in Miao and Wang [21]; our contribut...

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...

Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.