Convergence of partial differential equation using fuzzy linear parabolic derivatives

Abstract

Discovering solution for partial differential equations (PDEs) is considered to be difficult task. Exact solution is said to be identified only in certain specified cases. In this paper, convergence of partial differential equation using fuzzy linear parabolic (PDE-FLP) method on a finite domain is designed. The method is based on PDE where coefficients are obtained as fuzzy numbers and solved by linear parabolic derivatives. Firstly, PDE form and fuzzy representation of two independent variables are derived. Secondly, fuzzy linear parabolic (FLP) derivative is provided for numerical convergence. FLP derivatives are employed to describe time dependent aspects. Parabolic derivatives are also due to similar coefficient condition for the analytic solution. Finally, numerical results are given, which demonstrates the effectiveness and convergence of PDE-FLP method. A detailed comparison between approximate solutions obtained is discussed. Also, figurative representation to compare between approximate solutions is also presented.