On the accuracy of homotopy perturbation and variational iteration methods for lateral broadening of a monoenergetic proton beam

In this article, dispersion of a 60 MeV proton pencil beam at various depths in a muscle tissue was numerically investigated via solving a three dimensional Fokker-Planck equation using homotopy perturbation method (HPM) and variational iteration method (VIM). The accuracy of these methods was benchmarked by comparison the radial flux distribution of protons traversing different depths in the tissue with the data of the High Charge and Energy Transport (HZETRN) model and Monte Carlo simulations. Furthermore, the computed depth dose distributions obtained from the HPM and VIM for monoenergetic protons passing through a medium were compared with the results of GEANT4.5.2 code as well as the experimental data reported in the literature. The satisfactory agreement obtained from our computations shows the reliability and applicability of the HPM and VIM in our analysis.