Semi-Analytical Solution of Heat Equation in Fuzzy Environment

Abstract

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.

Approximate solution of time-fractional fuzzy partial differential equations

“…Example 1 Consider the following time-fractional fuzzy parabolic equation (Allahviranloo and Taheri 2009;Jameel 2014):…”

Comparison of fuzzy Adomian decomposition method with fuzzy VIM for solving fuzzy heat-like and wave-like equations with variable coefficients

“…Stepnicka and Valasek [54] introduced the numerical solution of partial differential equations (PDEs) with the help of a fuzzy transform. Jameel [39] studied the semianalytical solution of the heat equation in a fuzzy environment. Allahviranloo et al [10] have presented the fuzzy solutions for heat equation based on generalized Hukuhara differentiability.…”