Using Recursive Differential Equations - John Dunn, Consultant, Ambertec, P.E., P.C.
This circuit is a simple RC network being charged from a DC source for which a descriptive, first order differential equation is written and is then put into a software loop to simulate the actual process under consideration:
This first result is nothing unexpected. The output has an exponential waveshape. However, when we go to the next step of adding an AC source in series with the DC source, we see that the output waveform reflects the effects of both the DC and the AC excitation:
This analysis method can be applied to virtually any circuit, linear or non-linear, for which you can write the first order differential equation(s) and place those equations into a software loop.