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Adams methods

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Adams methods are a subset of the general family of multistep methods used for the numerical integration of initial value problems based on odes. Multistep methods benefit from the fact that the computation has been going on for a while and use previously computed values of the solution (BDF methods) or the right hand side (Adams methods) to approximate the solution at the next step.

Adams methods begin by the integral approach,

y^\prime = f(t,y)

y(t_{N+1}) = y(t_{n}) + \int_{t_n}^{t_{n+1}} y^\prime (t) dt =  \int_{t_n}^{t_{n+1}} f(t,y(t)) dt

Since f is unknown in the interval t_n to t_{n+1} it is approximated by an interpolating polynomial p(t) using the previously computed steps t_{n},t_{n-1},t_{n-2} ... and the current step at t_{n+1} if an implicit method is desired.

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