In the following, do NOT merely look the answers up in your notes. Learn these answers. (Make flash cards?)

PROBLEM:  For each method, state the following:

1. the number of times the slope function f is evaluated per step,
2. the global error, and
3. whether the method is implicit or explicit.

• the Euler method

• the implicit Euler method

• the trapezoidal method

• the modified Euler method

• the classical Runge-Kutta method
        Also, when was this method published?

• the Runge-Kutta-Fehlberg method
        Also, when was this method published?

• the Runge-Kutta-Verner method
        Also, when was this method published?
  

FOLLOW-UP QUESTIONS:

1. Which methods are predictor-corrector methods?

2. Which methods are adaptive stepsize methods?

3. Which methods allow us to estimate the errors as we do the calculations?

4. Which methods have a formula to compute an optimal stepsize h?

5. Which two methods are combined to obtain the modified Euler method?
   In what way are they combined? Be specific.

6. Which two methods are combined to obtain the trapezoidal method?
   In what way are they combined? Be specific.

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