Abstract—In this paper, we develop and analyze the use of the Variational Iteration Method (VIM) to find the semi- analytical solution for an initial value problem involving the fuzzy heat parabolic equation. VIM 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 VIM will be studied for fuzzy initial value problems involving partial parabolic differential equations. Also VIM will be constructed and formulated to obtain a semi-analytical solution of fuzzy heat equation by using the properties of fuzzy set theory. Numerical example involving fuzzy heat equation was solved to illustrate the capability of VIM in this regard. The numerical results that obtained by VIM were compared with the exact solution in the form of Table I-Table II and Fig. 1-Fig. 2.

Index Terms—Fuzzy numbers, fuzzy differential equations, fuzzy partial differential equations, variational iteration method, fuzzy heat equation.

A. F. Jameel is with School of Mathematical Sciences, University Science Malaysia, 11800 USM Penang, Malaysia (e-mail: kakarotte79@gmail.com).

Cite: A. F. Jameel, "Semi-Analytical Solution of Heat Equation in Fuzzy Environment," International Journal of Applied Physics and Mathematics vol. 4, no. 6, pp. 371-378, 2014.