An iterative method for solving a two-point boundary-value problem

Abstract

The purpose of this paper is to study the existence, uniqueness, and method of construction of a nonnegative solution as well as the question of criticality for a two-point boundary-value problem arising in the transport process of n different types of particles in a rod of finite length subjecting incident fluxes and internal source. A recursion formula is derived for the calculation of the maximal and the minimal solution which are the respective limits of a monotonically nonincreasing sequence and a monotonically nondecreasing sequence. The behavior of these sequences leads to a characterization for the criticality question of the transport problem. It is shown under some physically reasonable conditions that the minimal and maximal solutions coincide so that it leads to a uniqueness theorem.