| Summary: | The solution to the second-order fuzzy unsteady nonlinear partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite, unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level of the lake; thus, the aquifer is recharging from the lake. The fuzzy solution is presented by a simple algebraic equation transformed in a fourth-degree polynomial approximation for the head profiles. In order to solve this equation, the initial and boundary conditions, as well as the numerous soil properties, must be known. A fuzzy approach is used to solve the problem since the aforementioned auxiliary conditions are vulnerable to various types of uncertainty resulting from human and machine errors. The physical problem described by a partial differential equation and the generalized Hukuhara derivative and the application of this theory for the partial derivatives were chosen as solving methods. In order to evaluate the accuracy and effectiveness of the suggested fuzzy analytical method, this study compares the findings of fuzzy analysis to those obtained using the Runge–Kutta method. This comparison attests to the accuracy of the former. Additionally, this results in a fuzzy number for water level profiles as well as for the water volume variation, whose α-cuts, provide according to Possibility Theory, the water levels and the water volume confidence intervals with probability <i>p</i> = 1 − α.
|
|---|