Numerical Solution of the Problem of Anomalous Solute Transport in a Two-Dimensional Nonhomogeneous Porous Medium

3. NUMERICAL SOLUTION OF THE PROBLEM

To solve equation (7), we use the finite difference method. For this, we introduce the following grid [25, 26]

where are the grid steps in time, coordinates and , respectively.

To approximate (7), an implicit finite-difference scheme can be used. However, this makes the circuit very complex. Therefore, here we use an explicit difference scheme of the following form [27, 28]

(8)

Equation (8) is written in the form

(9)

Grid equation (9) is a recursive equation that allows you to calculate the solution step by step.

The difference initial condition has the form

(10)

The boundary conditions in the difference form are written in the form

(11a)

(11b)