Adams-Bashforth method ($y_{n+1}=y_n+h(3f_n-f_{n-1})/2$)

An explicit linear multistep method that integrates a polynomial extrapolation of the past derivative values. The displayed two-step member is second order in time: the linear interpolant through $f_{n-1},f_n$, integrated over the next step, gives coefficients $3/2,-1/2$. For a spatially discretized partial differential equation, the spatial error must also be included in the total local defect.