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