The presented study aimed to perform a qualitative analysis of two calculated solutions to Neumann boundary value problems for a bounded region using the partition method. The proposed author's solutions have simulated the distribution of electric potential in a rectangular conducting plate through which a direct current passes. A modification of the standard boundary conditions was considered; it involved taking into account the nonuniform current density on the contact surface. A comparison of the results of the application of theoretical computer models obtained on the basis of solutions to the Neumann problems and experimental measurements was carried out. A significant increase in the solution accuracy was shown to achieve near current contacts when using the modified boundary conditions relative to the standard ones. Moreover, the discrepancy between the results obtained by these two calculation methods in the middle region of the sample, turned out to be minimal.