A general linear multi-step method is given by:

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.scholarpedia.org/article/FitzHugh-Nagumo_model

http://www.cs.rpi.edu/~flaherje/pdf/ode5.pdf

http://en.wikipedia.org/wiki/Linear_multistep_method

http://de.wikipedia.org/wiki/Francis_Bashforth

http://en.wikipedia.org/wiki/Forest_Ray_Moulton

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

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