1. CSE245:Lecture12 Advisor: C.K. Cheng Date: 02/13/03

2. 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

3. Prediction and Correction (cont) Step2: correction iteratively,use x n i to get x n i+1 using Backward Euler or Trapezoidal If the method converges, the solution is

4. Stiff Function A stiff function:

5. 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)

6. Conservation of Charges Two way to write nodal equations: (1) (2) The law of charge conservation: (3) (4)

7. Conservation of Charges (cont) Example: Apply Forward Euler method to (1) and (2) Apply Forward Euler method to (2), then charge is not conserved

8. Example (cont) Apply Forward Euler method to (1), then charge is conserved Theorem: Any consistent multistep method conserves charge when applied to (1)