Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method

The solution of the complex neutron diffusion equations system of equations in a spherical
nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remark-
able approximation method that successfully solves different systems of diffusion equations, and in
this work, the system is solved for the first time using the approximation method. The considered
system of neutron diffusion equations consists of two consistent subsystems, where the first studies
the reactor and the multi-group subsystem of equations in the reactor core, and the other studies the
multi-group subsystem of equations in the reactor reflector; each subsystem can deal with any finite
number of neutron energy groups. The system is simplified numerically to a one-group bare and
reflected reactor, which is compared with the modified differential transform method; a two-group
bare reactor, which is compared with the residual power series method; a two-group reflected reactor,
which is compared with the classical method; and a four-group bare reactor compared with the
residual power series.