SOLUTION OF FUZZY HEAT EQUATIONS BY HOMOTOPY PERTURBATION METHOD (HPM)

In this paper, we develop and analyze the use of the Homotopy Perturbation Method (HPM) to find the approximate analytical solution for an initial value problem involving the fuzzy parabolic equation. HPM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The HPM will be studied for fuzzy initial value problems involving partial parabolic differential equations. Also HPM will be constructed and formulated to obtain an approximate analytical solution of fuzzy heat equation by using the properties of fuzzy set theory. The convergence theorem of this method in fuzzy case is presented and proved. Numerical examples involving fuzzy heat equation was solved to illustrate the capability of HPM in this regard. The numerical results that obtained by HPM were compared with the exact solution in the form of tables and figures.