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Let a = -1, and all other a = 0
Approximate f(t) with a Lagrange Interpolation polynomial p(t)
Solve the equation y' = p(t) exactly using separation of variables
Then the b 's are determined by solving: Zachary Meyer, Lindsay Stepan,
Jimmy Broomfield Adam-Moulton 2-step History The Method The Problem Is it Working? The Code References Questions John Couch Adams The Adams-Moulton methods are similar to the
Adams-Bashforth methods in that they are derived
in the same way
The steps are as follows: We applied the Adam-Moulton 2-step method
to the FitzHugh-Nagumo differential equations
This system of differential equations gives a simplified model to describe how action potentials are initiated and propagated in squid axon's. The equations are: We used AM 4-step method
to with small step size as our
true solution, and compared
It seemed that AM-2 worked well for this problem http://www.math.ku.edu/~xu/12f-Math781w/Lec12-28.pdf
http://www-history.mcs.st-andrews.ac.uk/Biographies/Adams.html Forest Ray Moulton Francis Bashforth John Couch Adams was the main contributor in the Adam-Bashforth and Adam-Moulton Methods
Graduated as the "Senior Wrangler" from Cambridge University in 1843
Was primarily interested in Astronomy. Submitted calculations for the discovery of Neptune.
There was a controversy between the British and French about the eventual discovery Francis Bashforth's name is given on the Adams-Bashforth method because the method was first applied to his differential equation that modeled Capillary action.
Graduated as the "Second Wrangler" from Cambridge University in 1843.
Was primarily interested in ballistics Forest Ray Moulton's name has been associated with he Adams-Moulton method because he discovered that it could be used with the Adam-Bashforth Method as a predictor-corrector method.
Graduated from Chicago University in 1899
Primarily interested in Astronomy s-1 i i Here is the Adams-Moulton 2-step Method