multistep method

A method that reuses several of the SOLUTION's own recent slopes, already computed at earlier steps, instead of computing several new slopes within the current step.

A multistep method advances $y_n$ to $y_{n+1}$ using $f$ evaluated at several of the PREVIOUS grid points ( $f_n, f_{n-1}, f_{n-2}, \ldots$ ) rather than at new points within the current step (a Runge-Kutta method's own approach) -- an explicit multistep method (Adams-Bashforth) needs only that history; an implicit one (Adams-Moulton) also involves $f_{n+1}$ , evaluated at the very point being solved for. Every multistep method needs its first several starting values supplied by something else, since there's no history yet to build from at the start of a run -- in this course, always RK4.

Examples

A 2-step Adams-Bashforth method reuses $f_n$ and $f_{n-1}$ -- both already computed on earlier steps -- instead of evaluating $f$ at any new point within the current step.