On the p-Adic analog of Richards’ equation with the finite difference method

In this paper, with the help of a variant of Schauder fixed point theorem in the real Banach algebra together with the finite difference method (FDM), we take a brief look at the [Formula: see text]-adic analog of Richards’ equation derived by Khrennikov et al. [Application of [Formula: see text]-adic wavelets to model reaction–diffusion dynamics in random porous media, J. Fourier Anal. Appl. 22 (2016) 809–822], and study the solvability and solution of this problem. This equation is formulated by a kinetic equation during the modeling of the reaction–diffusion dynamics in random porous media. Moreover, in order to guarantee the convergence of the presented iterative schemes, some sufficient conditions would be presented.