The time-stepper or time-integration module is perhaps the core of the simulator. It determines most of the numerical methods that will be applied to solve the mono- or bi-domain problem (the most notable exception being the numerical method to solve the linear systems). The time-integrator also determines the overall accuracy of the simulation. When we say that an algorithm has O(h) accuracy for time-step size h, we are referring to the accuracy of the time-integrator. For O(h) accuracy, we expect that cutting the time-step size in half, the given time-stepper will produce output that is twice as accurate. Other time-steppers may be O(h^2) or O(h^4) accurate, indicating that halving the time-step size should produce 4 times or 16 times more accuracy in the output, respectively. Thus, higher order time-integration schemes can use larger time-step sizes and still retain usable accuracy. Of course, this must be balanced with the additional complexity and run-time that the higher-order methods may require.
