A Simple Approach for Explicit Solution of The Neutron Diffusion Kinetic System

Abstract

This paper introduces a new approach to directly solve a system of two coupled partial differential equations (PDEs) subjected to physical conditions describing the diffusion kinetic problem with one delayed neutron precursor concentration in Cartesian geometry. In literature, many difficulties arise when dealing with the current model using various numerical/analytical approaches. Normally, mathematicians search for simple but effective methods to solve their physical models. This work aims to introduce a new approach to directly solve the model under investigation. The present approach suggests to transform the given PDEs to a system of linear ordinary differential equations (ODEs). The solution of this system of ODEs is obtained by a simple analytical procedure. In addition, the solution of the original system of PDEs is determined in explicit form. The main advantage of the current approach is that it avoided the use of any natural transformations such as the Laplace transform in the literature. It also gives the solution in a direct manner; hence, the massive computational work of other numerical/analytical approaches is avoided. Hence, the proposed method is effective and simpler than those previously published in the literature. Moreover, the proposed approach can be further extended and applied to solve other kinds of diffusion kinetic problems.