In this paper, numerical solution of two points 2 order nonlinear boundary-value problems was considered. The numerical solution was reviewed with nonlinear shooting method, finite-difference method and fourth order compact method. The results were compared to check the accuracy of numerical schemes with exact solution. It was found that the nonlinear shooting method is more accurate than finit...

The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP). In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,R). Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can i...

We introduce a new approach for analysis and numerical simulations of asymmetric first-price auctions, which is based on dynamical systems. We apply this approach to asymmetric auctions in which players’ valuations are power-law distributed. We utilize a dynamical-systems formulation to provide a proof of the existence and uniqueness of the equilibrium strategies in the cases of two coalitions ...

with zi ∈ { Ĉ[0, T ] |zi(0) = 0, zi(T ) = bi } , with technical constraints for the consumption rate over time: mi ≤ żi(t) ≤Mi, ∀i = 1, . . . , n. We abstract from this situation to tackle a general problem which studies a production process whose efficiency of production with respect to each input depends on time, on the stock of the various inputs, and on the consumption rate of other inputs....

The problem of steady Marangoni boundary layer flow and heat transfer in a nanofluid when the wall is permeable, namely there is a suction or injection effect, is studied using different types of nanoparticles. The mathematical problem reduces to a pair of coupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Three diff...

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shoo...

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is...

—As the use of UAV (Unmanned Aerial Vehicle) such as drone has been increased recently, aerial video shooting technology and surveillance system began to attract global attention. The video surveillance system using an UAV requires high speed wireless transmission technology to obtain high resolution video images in real-time under poor on-air channel environment, accurate positioning trace te...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning...