(Difference between revisions)
 Revision as of 23:57, 9 December 2005 (view source)← Older edit Revision as of 23:57, 9 December 2005 (view source)Newer edit → Line 9: Line 9: :$:[itex] - y(t_{N+1}) = y(t_{n}) + \int_{t_n}^{t_{n+1}} y^\prime (s) ds = \int_{t_n}^{t_{n+1}} f(s,y(s)) ds + y(t_{N+1}) = y(t_{n}) + \int_{t_n}^{t_{n+1}} y^\prime (t) dt = \int_{t_n}^{t_{n+1}} f(t,y(t)) dt$ [/itex]

## Revision as of 23:57, 9 December 2005

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,

$y^\prime = f(t,y)$

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