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WOLFRAM LANGUAGE FEATURED EXAMPLE

RLC Circuit Driven by 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 a 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 with the mean function:
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Compute the variance function:
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Simulate the model using a strong order 1.5 Kloeden–Platen–Schurz scheme:
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Visualize simulated paths:
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Visualize a 95% confidence band about the mean function:
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Combine the plots together.
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