Adams methods
From CFD-Wiki
Adams methods are a subset of the family of multistep methods used for the numerical integration of initial value problems based on 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,
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.