Soft Numerical Computing in Uncertain Dynamic Systems

7.4: Fuzzy finite difference method for solving the fuzzy Poisson's equation

In this section, first, the fuzzy Poisson's equation and the fuzzy finite difference method are introduced. Then, the fuzzy Poisson's equation is discretized by fuzzy finite difference method and it is solved as a linear system of equations. In addition, we discuss fuzzy Laplace equation as a special case of the fuzzy Poisson's equation. Finally, the convergence of method is considered and for more illustration, a numerical example is solved.

Numerous problems in industry have led to an equation with a fuzzy partial differential equation in the following form:

$\mathrm{\Delta }u\left(x,y\right)=f\left(x,y\right)\text{in}\mathrm{\Omega }$

in which Ω = {(x, y)| 0 ≤ x, y ≤ 1} is regular area, and the operator Δ is defined as:

$\mathrm{\Delta }u\left(x,y\right)$