The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions Chein-Shan Liu1 Summary The present paper provides a Lie-group shooting method for the numerical solutions of second-order nonlinear boundary value problems exhibiting multiple solutions. It aims to find all solutions as easy as possible. The boundary conditions considered are classified ...

Differential equation modeling is central to applications of mathematics to science and engineering. When a particular system of equations is used in an application, it is often important to determine unknown parameters. We compare the traditional shooting method to versions of multiple shooting methods in chaotic systems with noise added and conduct numerical experiments as to the reliability ...

We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness the number of iterations required to give convergent results of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validat...

We show that nonlinear Liouville theorems does not hold in general for indefinite problems on half spaces. Thus, in order to use blow-up method to obtain a priori estimates of indefinite elliptic equations, one has to impose assumptions on the nodal set of nonlinearity. The counter example is constructed by shooting method in one-dimensional case and then extended to higher dimensions.

In this overview paper, we first survey numerical approaches to solve nonlinear optimal control problems, and second, we present our most recent algorithmic developments for real-time optimization in nonlinear model predictive control. In the survey part, we discuss three direct optimal control approaches in detail: (i) single shooting, (ii) collocation, and (iii) multiple shooting, and we spec...

This paper studies a new approach to analyze the large deflection behavior of prismatic and non-prismatic beams of non-homogenous material under combined load and multiple boundary conditions. The mathematical formulation has been derived which led to a set of six first-order ordinary differential equations. The geometric nonlinearity was solved numerically using the multiple shooting method co...

Estimating the parameters of a dynamical system based on measurement data is an important but complex task in industrial and scientific practice (Schittkowski, 2002). Due to its importance, different approaches to solve this kind of problem have been developed. The most established ones are single shooting (Bard, 1974), multiple shooting (Bock, 1983) and full discretization techniques (Biegler,...

The multiple shooting method has proved to be a very reliable and eecient method for the solution of multipoint boundary value problems such as those obtained from the necessary conditions for the solutions of constrained optimal control problems. If this technique is also to be used for guidance purposes, special features have to be implemented to reach a computing speed which enables real-tim...

In the study of mechanics and optimal control, one often encounters what is called a two-point boundary-value problem (TPBVP). A couple of methods exist for solving these problems, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM). In this paper a new method is proposed that was designed from the favorable aspects of both the SSM and the MSM. The Mod...