RLC Circuit Driven by a Periodic Signal and White Noise
Consider an electrical circuit consisting of a resistor, inductor, and capacitor connected in series. The circuit is under external voltage, which is a superposition of a periodic signal and white noise.
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Define the parameters of the model.
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Compute the mean function, i.e. the mean value of the charge of the capacitor as a function of time.
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Solve the deterministic problem in the absence of noise and compare it with the mean function.
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Compute the variance function.
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Simulate the model using the strong Kloeden-Platen-Schurz scheme of order .
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Visualize the simulated paths.
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Visualize a 95% confidence band about the mean function.