We prove existence and uniqueness (up to rescaling) of positive radial entire solutions of supercritical semilinear biharmonic equations. The proof is performed with a shooting method which uses the value of the second derivative at the origin as a parameter. This method also enables us to find finite time blow up solutions. Finally, we study the convergence at infinity of regular solutions tow...

Abstract In this paper, the ascent trajectory optimization of a lifting body Single-Stage To Orbit (SSTO) reusable launch vehicle is investigated. The work carried out using Direct Multiple Shooting method to solve Optimal Control problem. crucial initialisation optimisation process performed by combination two evolutionary algorithms, namely Multi-Objective Parzen-based Estimation Distribution...

The parareal algorithm is a method to solve time-dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on new convergence results that show supe...

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...

We propose a method for the estimation of parameters of nonlinear delayed feedback systems from a time series. Being based on the multiple shooting approach it is fairly robust against high levels of observation noise and yields precise parameter estimates. We evaluate its performance using simulated data of the Mackey–Glass equation and present an application to observed time series of an elec...

Trajectory optimization is an important means to improve performance in many industrial and scientiic processes such as robotics or aerospace applications. A combination of SQP methods with direct collocation or multiple shooting discretizations has proven very successful for such problems. In realistic applications, however, very large QP sub-problems with thousands of constraints may arise. T...

In silico investigations by simulating dynamical models of biochemical processes play an important role in systems biology. If the parameters of a model are unknown, results from simulation studies can be misleading. Such a scenario can be avoided by estimating the parameters before analysing the system. Almost all approaches for estimating parameters in ordinary differential equations have eit...

This work is an example of application of nonlinear programming to a problem of three-dimensional trajectory optimization for multistage launch vehicles for geostationary orbit missions. The main objective is to minimize fuel consumption or equivalently to maximize the payload. The launch vehicle considered here, Europa-II, consists of 5 thrust phases and 2 coast phases. Major parameters of the...

Energy efficient train control has been an active field of research for several decades, with Pontryagin’s maximum principle and dynamic programming being the two most common approaches computation optimal trajectories. In this paper, we detail how direct multiple shooting can be used in same context highlight its main advantages: flexibility problem formulation availability computationally ope...