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Adams methods

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Adam's methods are a subset of the family of multistep methods used for the numerical integration of initial value problems in ODEs. Multistep methods benefit from the fact that the computations have been going on for some time, 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.
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Adams' methods are a subset of the family of multistep methods used for the numerical integration of initial value problems in ODEs. Multistep methods benefit from the fact that the computations have been going on for some time, 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,
Adams' methods begin by the integral approach,

Revision as of 03:23, 10 December 2005

Adams' methods are a subset of the family of multistep methods used for the numerical integration of initial value problems in ODEs. Multistep methods benefit from the fact that the computations have been going on for some time, 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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