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In this paper, it is a question of identification of the parameters in the equation ofRichards modelling the flow in unsaturated porous medium. The mixed formulation pressure head-moisture content has been used. The direct problem was solved using Multiquadratic Radial Basis Function ( RBF-MQ ) method which is a meshless method. The Newton-Raphson’s method was used to linearize the equation. The function cost used is built by using the infiltration. The optimization method used is a meta-heuristic called Modified hybrid Grey Wolf Optimizer -Genetic Algorithm (HmGWOGA). A test on experimental data has been carried. We compared the results with genetic algorithms. The results showed that this new method was better than genetic algorithms.

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We study homogenization and two-scale convergence. Homogenization is a mathematical concept that makes it possible to develop a global model of the behaviour of a physical structure evolving in a heterogeneous structure. The behaviour of this physical structure will therefore be studied in a homogeneous environment, which greatly facilitates calculations. The two-scale convergence method was introduced by Nguetseng and later developed by Allaire. It is a particular form of weak convergence, a convergence between weak convergence GÉRARD ZONGO et al. 54 and strong convergence. The two-scale convergence simplifies the proof of homogenization theory. The method evolved very quickly and has been extended to several cases depending on the functional space.

This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow -up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.