Abstract
The solution of neutron diffusion equation is important to describe the behavior of the neutrons in the nuclear reactors. The essential cylindrical reactor geometry will be studied in this work, where the reactor reflector part is added to the core part to minimize its critical radius, and the neutrons diffuse in two different velocities. The massive results when diversification of the appropriate new approaching technique of homotopy perturbation method (HPM) represent its flexibility and suitability to deal with different nuclear reactor boundary conditions. To assure our results, a comparison with classical results and transport theory data has been achieved which made after needed simplification to one velocity case. The necessary C+ + codes using GSL library are accomplished to attain this comparison.