CSE245:Lecture12

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CSE245Lecture12

• Advisor C.K. Cheng
• Date 02/13/03

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Prediction and Correction

• Predictor-corrector method
• Apply to solve implicit integration methods as
  backward Euler, trapezoidal
• Step1 prediction, predict an initial value by
  Forward Euler

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Prediction and Correction(cont)

• Step2 correction iteratively,use xni to get
  xni1 using Backward Euler or Trapezoidal
• If the method converges, the solution is

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Stiff Function

• A stiff function

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Stiff Function(cont)

• To see the effect of the second item, the
  stepsize should be small as
• Stiff function happens in
• Interconnect network
• Modulator
• PLL (phase lock loop)

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Conservation of Charges

• Two way to write nodal equations
• (1)
• (2)
• The law of charge conservation
• (3)
• (4)

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Conservation of Charges(cont)

• Example Apply Forward Euler method to (1) and
  (2)
• Apply Forward Euler method to (2), then charge is
  not conserved

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Example(cont)

• Apply Forward Euler method to (1), then charge is
  conserved
• Theorem Any consistent multistep method
  conserves charge when applied to (1)