Numerical solutions of fuzzy partial differential equations and its application in heat transfer problem

Calculation of the solution of fuzzy partial differential equations is in general very difficult. We can find the exact solution only in some special cases. Fortunately, in most of mathematical applications relations between the solutions and uncertain parameters are monotone. In this case, the exact solution can be calculated using only endpoints of given intervals. In this paper, a very efficient algorithm of solution was presented. This algorithm is based on finite element method (FEM) and sensitivity analysis. Using this method we can solve heat transfer problem with thousands degree of freedom.

Keywords:

fuzzy sets , finite element method , heat transfer problem , fuzzy partial differential equations