In this article we consider the problem −∆pu − b (x) |∇u| p−1 = a (x) f (u) , u > 0 on R (N ≥ 3), lim|x|→∞ u(x) = 0. We prove that the considered problem has a bounded positive entire radial solution under some conditions on a, b and f . The method of proving theorems is essentially based on the shooting method. Our result, about the existence of radially symmetric solutions, seem to be the fir...

The method devised by Lewis et al. (1993) for calculating the light curve of a microlensed point source is expanded to two dimensions to enable the calculation of light curves of extended sources. This method is significantly faster than the ray shooting method that has been used in the past. The increased efficiency is used to obtain much higher resolution light curves over increased time scal...

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 ...

The shooting method is a numerically effective approach to solving certain eigenvalue problems, such as that arising from the Schrödinger equation for the two-dimensional hydrogen atom with logarithmic potential function. However, no complete proof of its rationale and correctness has been given until now. This paper gives the proof, in a generalized form.

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...

B Abstract. Recently, in a paper of Chylla and Haase 2], a model of a multi-product semibatch polymerization reactor has been developed which is representative of those found in the speciality chemical processing industry. One of the aims in these processes is to keep a certain reaction temperature setpoint, in order to t the quality requirements for the polymer. In the present paper, the optim...

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...

Chemical processes are modeled by large-scale, highly-nonlinear process models often governed by unstable dynamics. Dynamic optimization is required to exploit economical performance of these processes in their unstable regions. On the one hand, direct single shooting is able to solve large-scale dynamic optimization problems, but lacks the ability to cope properly with unstable dynamical syste...

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in L...

This paper presents a Lie-group shooting method for the numerical solutions of multi-dimensional nonlinear boundary-value problems, which may exhibit multiple solutions. The Lie-group shooting method is a powerful technique to search unknown initial conditions through a single parameter, which is determined by matching the multiple targets through a minimum of an appropriately defined measure o...