What kind of variable is your input? What is its role in your problem? I dare to guess (based on some other private discussion we had) that it is actually a control variable.
If I am right, then most often than not this control variable (some might call it manipulated variable) will be periodically produced by a discrete-time (computer) controller. The variable will then be piecewise constant and the simulation should capture this. There was already some discussion of this here: