The turbulent filtration equation in porous media is a very important equation which has many applications to solve the problems appearing especially in fluid mechanic. Many applied mechanical problems can be solved using this equation. For example, non-Newtonian mechanical filtration equation, which is a very important equation in fluid mechanic, is a special case of this equation. In this paper, several numerical solutions are presented to solve the turbulent filtration equation and its special cases such as the non-Newtonian mechanical filtration equation. The proposed discrete numerical solutions will be simulated using the Matlab software to proof that the proposed numerical solutions are realizable.

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