Epilepsy is a neurological disorder in which patients have recurrent seizures. Seizures occur in conjunction with abnormal electrical brain activity which can be recorded by the electroencephalogram (EEG). Often, this abnormal brain activity consists of high amplitude regular spike-wave oscillations as opposed to low amplitude irregular oscillations in the non-seizure state. Active brain stimulation has been proposed as a method to terminate seizures prematurely, however, a general and widely-applicable approach to optimal stimulation protocols is still lacking. In this study we use a computational model of epileptic spike-wave dynamics to evaluate the effectiveness of a pseudospectral method to simulated seizure abatement. We incorporate brain connectivity derived from magnetic resonance imaging of a subject with idiopathic generalized epilepsy. We find that the pseudospectral method can successfully generate time-varying stimuli that abate simulated seizures, even when including heterogeneous patient specific brain connectivity. The strength of the stimulus required varies in different brain areas. Our results suggest that seizure abatement, modeled as an optimal control problem and solved with the pseudospectral method, offers an attractive approach to treatment for in vivo stimulation techniques. Further, if optimal brain stimulation protocols are to be experimentally successful, then the heterogeneity of cortical connectivity should be accounted for in the development of those protocols and thus more spatially localized solutions may be preferable.