A semi-implicit spectral/finite difference technique is used to evolve a reduced set of the visco-resistive MHD equations to investigate nonlinear processes involving reconnection on a planar current sheet. Two particular cases, of interest in astrophysical and magnetically confined plasmas, are discussed. An investigation of the time asymptotic behaviour of the basic current sheet with periodic boundary conditions and a cosh2x resistivity dependence has revealed a sequence of symmetry breaking bifurcations as a function of a parameter, Lp, defined as the ratio of the periodicity length of the system to the characteristic half-width of the current channel. Details are given of the dynamical behaviour involving coalescence and secondary current sheet instability. A method for periodically perturbing the edge magnetic field in the presence of flow without generating unphysical viscous boundary layers was then introduced to investigate forced reconnection in a stable plasma with finite flow along the current sheet. As the flow velocity was increased from zero, a transition from a state with force reconnected magnetic islands to one with negligibly small islands occured around a value of the velocity that depended on the Lunquist number and the viscosity.