Fuzzy numerical solution to the unconfined aquifer problem under the Boussinesq equation

In this article, the fuzzy numerical solution of the linearized one dimensional Boussinesq equation of unsteady flow in a semi-infinite unconfined aquifer bordering a lake is examined. The equation describing the problem is a partial differential parabolic equation of second order. This equation requires the knowledge of the initial and boundary conditions as well as the various soil parameters. The above auxiliary conditions are subject to different kinds of uncertainty due to human and machine imprecision and create ambiguities to the solution of the problem and a fuzzy method is introduced. Since the physical problem refers to a partial differential equation, the generalized Hukuhara (gH) derivative was used, as well as the extension of this theory regarding the partial derivatives. The objective of this paper is to compare the fuzzy numerical and analytical results, for two different cases of physical problem of aquifer’s unsteady flow, in order to prove the reliability and efficiency of the proposed fuzzy numerical scheme (fuzzy Crank-Nicolson scheme). The comparison of the methods was based on the transformed Haussdorf metric, presented that the distances between the analytical and numerical results tend to zero.