Backward differentiation formula

Summary

A backward differentiation formula, or BDF method, is an implicit linear multistep method. It differentiates the polynomial through the latest computed values and sets its slope at the new point equal to $f$. The $k$-step formula has order $k$, and it is zero-stable only for $k \le 6$. Because of their large regions of stability, BDF methods are the standard methods for stiff equations. The one-step formula is the backward Euler method.