Numerical Solutions of Heat Diffusion Equation Over One Dimensional Rod Region

Abstract

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.