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Adaptive methods for derivation of analytical and numerical solutions of heatdiffusion in one dimensional thin rod have investigated. Comperhensivecomparsion analysis based on the homotopy perturbation method (HPM) and finitedifference method (FDM) have been applied to the rod PDE system. The resultsshow that performing HPM will eventuate more precision and satisfactoryapproximations at reasonable time than those obtained from FDM when compared toexact solution results. Also since solutions are originated from the problemsin HPM thus it is convenient to express them with different functions whichconclude that homotopy perturbation is a powerful numerical technique forsolving partial differential equations.

Numerical Solutions of Heat Diffusion Equation Over One Dimensional Rod Region