Magnetic reconnection is a strong candidate for a coronal heating mechanism, and heating by forced magnetic reconnection is investigated here. Two dimensional, nonlinear magnetohydrodynamic simulations are used to investigate forced magnetic reconnection in a compressible plasma. The reconnection occurs when a sheared force-free field is perturbed by a slow disturbance (pulse) at the boundary which is representative of the solar corona where the reconnection is induced by the photospheric motions. The case of driving by successive pulses, which generate a series of heating events which may interact with each other, is considered. This is in order to model the heating of the corona by a series of nanoflare events. For small perturbations, the simulation results are consistent with the previous analytic theory based on linear approach where a current sheet is formed initially at the resonant surface followed by reconnection and then release of magnetic energy. For large amplitude perturbations, or close to the threshold for tearing instability, the system exhibits strong nonlinear aspects. Following the second driving pulse, the current sheet expands along the separatrix before relaxing to a reconnective equilibrium and releasing even more magnetic energy for the same amplitude perturbation.