Positive solutions to the nonlinear reactor model by variational iteration method

Abstract

We investigate the equation of the form (a(t)u^{prime }(t))^{prime }+Aa(t)u^{prime }(t)+f(t,u(t))=0 a.e. in (0, 1) with boundary conditions u^{prime }(0)=0,u^{prime }(1)+Au(1)=0, which is associated with the classical Markus and Amundson’s model. The main goal of this paper is to show that He’s variational iteration method appears to be very useful in deriving formulas of approximate solutions and gives better results that other methods. This fact will be illustrated by a few representative examples of BVPs of the aforementioned type. The numerical part is preceded by the theoretical results devoted to existence of positive solutions to this problem and their properties. We also discuss the dependence of the solutions on functional parameters. Our approach allows us to consider sublinear and superlinear cases in which f can be singular with respect to the first variable.