In the last years, fractional calculus has been used to model the propagation of non-linear waves in fluid saturated porous media. We solve numerically a model parabolic system, based on Caputo fractional non-local Darcy law. We apply weighted difference schemes to derive discrete approximations and to describe the mechanical picture of the model. Picard iterative method is realized for fast solving the non-linear systems of difference equations. Exact solution test example with geophysical parameters illustrate the efficiency of the numerical method.
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