In this paper we present the numerical solution of the problem 2-D unsteady free convective heat and mass transfer flow over a moving semi-infinite vertical porous plate with thermal diffusion in presence of magnetic field, dissipative heat and Soret effects taking into account the induced magnetic field. The steady-state numerical solutions for the velocity field, induced magnetic field, temperature distribution and concentration distribution are obtained by the explicit finite difference method and the network simulation method. The obtained results have been shown graphically. The obtained numerical results were compared with other author data to demonstrate the efficiency of the method used, moreover all the cases the convergence is always quickly reached. An increase in Soret or Eckert number is found to strongly enhance the fluid velocity and temperature values, and this effect is reversed for the induced magnetic field. It is found that the flow velocity decreases with the increase in Hartmann and magnetic Prandtl number, and an opposite behaviour is observed for the fluid temperature. Applications of the study arise in the thermal plasma reactor modelling, the electromagnetic induction, MHD transport phenomena in chromatographic systems, and the magnetic field control of materials processing. The results show that both methods provide excellent approximations to the solution of this nonlinear system with high accuracy. (C) 2017 Elsevier Ltd. All rights reserved.