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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