  Adaptive methods for derivation of analytical and numerical solutions of heat
diffusion in one dimensional thin rod have investigated. Comperhensive
comparsion analysis based on the homotopy perturbation method (HPM) and finite
difference method (FDM) have been applied to the rod PDE system. The results
show that performing HPM will eventuate more precision and satisfactory
approximations at reasonable time than those obtained from FDM when compared to
exact solution results. Also since solutions are originated from the problems
in HPM thus it is convenient to express them with different functions which
conclude that homotopy perturbation is a powerful numerical technique for
solving partial differential equations.
