Chapter 7: Numerical solutions of uncertain partial differential equations
Abstract
In this chapter, first, fuzzy heat and Poisson equations with fuzzy initial values are considered. The concept of generalized Hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases. The first objective of this chapter is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions. Then the fuzzy Fourier transform is applied for solving the fuzzy heat equation.
As the second object, the fuzzy Poisson's equation and the fuzzy finite difference method are introduced. ...
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