We present the numerical solutions of optimality systems corresponding to optimal control problems governed by the mono-domain equations which are widely used for describing the electrical activity of the cardiac tissue. This mono-domain model is based on a parabolic equation and a system of stiff ordinary differential equations. The space discretization of the state variables and dual variables is done using piecewise linear finite elements and the time discretization is based on linearly implicit Runge-Kutta methods. The main goal of this work is to study the optimal control behavior of the electrical potentials under the influence of extracellular ionic currents as control variables. The numerical results presented are based on first and second order optimization methods. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)