Adams methods
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| - | Since <math>f</math> is unknown in the interval <math>t_n</math> to <math>t_{n+1}</math> it is approximated by an interpolating [[polynomial]] <math>p(t)</math> using the previously computed steps <math>t_{n},t_{n-1},t_{n-2} ...</math> | + | Since <math>f</math> is unknown in the interval <math>t_n</math> to <math>t_{n+1}</math> it is approximated by an interpolating [[polynomial]] <math>p(t)</math> using the previously computed steps <math>t_{n},t_{n-1},t_{n-2} ...</math> and the current step at <math>t_{n+1}</math> if an implicit method is desired. |
Revision as of 00:01, 10 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,
Since 
is unknown in the interval 
to 
it is approximated by an interpolating polynomial 
using the previously computed steps 
and the current step at if an implicit method is desired.
