Application of The Homotopy Perturbation Method to the Neutron Diffusion Equation

Abstract

The Homotopy Perturbation Method (HPM) has been shown to be effective in solving both linear and nonlinear differential equations in mathematics, making it useful in a wide range of applications in the fields of physics and engineering. In this study, the Homotopy Perturbation Method was applied to the neutron diffusion equation for a one-dimensional time-independent approach. The Laplace operator of the neutron diffusion equation was considered for Cartesian, spherical and cylindrical coordinates. The critical radius values obtained for three different systems were calculated for all possible values of the relevant material parameter B. The results show that the solution of the neutron diffusion equation is agree with the literature.