A two dimensional model under uniform resistivity was studied for incompressible plasma. The dynamical equations governing the time evolution of the system was derived using basic theory in electrodynamics and fluid mechanics. A computer code to simulate the reconnection was developed with an explicit finite difference method as the discretization scheme. The boundary condition for the plasma inflow region was implemented adhering to the global magnetic field geometry while the plasma was allowed to freely exit from the outflow region. The use of open conditions in the outgoing boundary provided simplicity and confirmation that the steady state results did not depend much on the dynamics in the seperatrix region. The steady state results were found to be consistent with the Sweet-Parker theory regardless of the starting conditions. The set of solutions for the field and velocity distributions across the grid are presented for a typical set of parameters. A mean reconnection rate representative expressed as a factor times the Sweet-Parker rate is introduced in accordance with the uniform electric field at steady state. Steady state rates are obtained as (1.12 ±0.02)ESP and (1.24 ±0.08)ESP for Sweet-Parker type and Petschek type set of initial conditions respectively. If much higher reconnection rates were possible, they present themselves as new characteristics in solutions such as the current density. No characteristics deviating from the Sweet-Parker solution was observed in this study, even the initially set up Petschek shock structures dissolved with time. Parameter variations were done to test the performance of the model and optimal ranges were determined. The variations of the solution in the mid-plane under parameter changes were studied in detail.
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