Weeks 6-8 Questions

Class Procedures

Are we going to have to know the Forward Euler, Crank-Nicholson, Runge-Kutta, Adams- Bashford, and Adams-Moulton Formulas.

Know the Forward and Backward Euler formulas, and Crank-Nicholson cold. Understand how to use them to move from the approximation to the solution at one time to the approximation at a small step in time later. Know which of these is always stable (Backward Euler), and the characteristics of an instability in Forward Euler. Know the difference in accuracy between Euler and Crank-Nicholson. Know that Runge-Kutta, Adams-Bashford, and Adams-Moulton are substantially more accurate in a formal sense (fourth order). Associate these later 3 names with higher accuracy, and the potential for instability if not used carefully, but do not attempt to memorize the formulae.

Can you provide a supplement work-out review so that we can try a wider range of problems?

Here's two:

Write the ODE solution step in Homework 15 with Forward Euler.

Write the ODE solution step in Homework 15 with Backward Euler

I'll see what can be put on the Web by the end of the week.

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