Green’s Function Method for Solving BVP of Class Elliptic-Type Fuzzy PDEs

Elliptic fuzzy PDEs bridge deterministic models and real-world uncertainty, enabling rigorous modelling of steady-state systems with imprecise parameters. The Green’s function method has been widely recognized as an effective technique for investigating boundary value problems associated with the Poisson and Laplace equations. This method relies on the principle of superposition: a complex field source is decomposed into a superposition of several simple point or line sources. Once the field produced by a point source is known, the field generated by an arbitrary source can be computed via superposition. In the present study, the Green’s function method is primarily applied to solve the first boundary value problems for both the fuzzy Laplace equation and the fuzzy Poisson equation. Furthermore, we derive the fundamental integral formulation for the fuzzy Poisson and Laplace equations. At the same time, the fundamental integral formulation is used to obtain the solutions of the fuzzy Poisson and fuzzy Laplace equations. Several illustrative examples are also provided to demonstrate the solution procedure for these BVPs using the Green’s function method.