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Example Question #1 : Multi Step Methods
The two-step Adams-Bashforth method of approximation uses the approximation scheme .
Given that and , use the Adams-Bashforth method to approximate for with a step size of
In this problem, we're given two points, so we can start plugging in immediately. If we were not, we could approximate by using the explicit Euler method on .
Plugging into , we have
Note, our approximation likely won't be very good with such large a time step, but the process doesn't change regardless of the accuracy.