We can derive an exact solution of the discrete equations

• We have a linear, homogeneous, difference equation for $u^n$.
• Has solutions $u^n \sim IA^n$, where $A$ is unknown (number).
• Here: $\uex(t) =I\cos(\omega t) \sim I\exp{(i\omega t)} = I(e^{i\omega\Delta t})^n$
• Trick for simplifying the algebra: $u^n = IA^n$, with $A=\exp{(i\tilde\omega\Delta t)}$, then find $\tilde\omega$
• $\tilde\omega$: unknown numerical frequency (easier to calculate than $A$)
• $\omega - \tilde\omega$ is the phase error
• Use the real part as the physical relevant part of a complex expression