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Fuzzy solution of nonlinear Boussinesq equation

Profile image of Christos TzimopoulosChristos Tzimopoulos

Journal of Hydroinformatics

https://doi.org/10.2166/HYDRO.2022.026
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Abstract

In this paper, the solution of the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite unconfined aquifer bordering a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake's water level, thus the aquifer is recharging from the lake. The aquifer boundary conditions are considered fuzzy and, therefore, ambiguities are created to the solution of the overall physical problem. Then, the fuzzy problem is translated to a system of crisp boundary value problems. By using a Boltzmann transformation, the crisp problem is transformed into an integro-differential equation and solved with the help of a special numerical method. This method has a simple iterative procedure, which converges rapidly and is proven very accurate in comparison with other analytical methods. Additionally, the algebraic equation estimates very close to the st...

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