In this work we present a numerical study of a non-linear space-fractional parabolic system, describing thermoelastic waves propagation in fluid saturated porous media with non-local Darcy law. We use implicit cell-centered finite difference method for numerical discretizations, combined with L1- 2 formula for the fractional derivative approximation. We apply Newton's method to compute the finite difference solution. We solve a linear system of algebraic equation in block-matrix form on each iteration, using Schur complement. Numerical experiments attest good attributes of the proposed numerical method.
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