A Novel Ansatz Method for Solving the Neutron Diffusion System in Cartesian Geometry

This paper analyzes the system of partial differential equations (PDEs) describing the diffusion kinetic problem with one delayed neutron precursor concentration in Cartesian geometry. The neutron diffusion kinetic equation is a popular problem in the fundamental Physics which is of practical applications in both nuclear physics and reactor design. For safety considerations, accurate solution of the this fundamental problem is required and mandatory. However, many difficulties arise when dealing with the current model using various numerical/analytical approaches as can be noticed in the literature. So, it is the objective of this paper to develop a new ansatz method to directly solve such fundamental model. It is shown in this work that our approach is straightforward and simpler when compared with other approaches in the relevant literature.