A model for the dynamics of the length distribution in polymer bundles is presented. It considers nucleation, polymerization, and depolymerization and is derived as a continuous macroscopic limit from a discrete description. Its main feature is a nonlinear coupling due to competition of the depolymerizing ends for the limited supply of a depolymerization agent. The model takes the form of an in...

It is well known that the problem of estimating the state and parameters of discrete-time nonlinear dynamic systems from noisy measurements can be formulated as a nonlinear two-point boundaryvalue problem. In this paper, an algorithm is developed for solving the above boundary-value problem. The algorithm, which is based on Newton's method, requires very little storage. A detailed discussion of...

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

We consider nonlinear boundary value problems with multiple solutions. A method is proposed for the computation of such solutions which depends crucially on known a priori qualitative information about the behavior of the solutions. The method is a two-stage method where the second stage is a shooting method and initial values of the shooting parameters are found in a first stage which approxim...