Linear multistep method

Summary

A linear multistep method solves an initial value problem $y' = f(t, y)$ numerically. It computes the next approximation from a fixed number of earlier approximations and the values of $f$ there. It needs only one new evaluation of $f$ per step, which makes it cheap compared with Runge–Kutta methods of the same order. The Adams methods and the backward differentiation formulas are the main families. Its convergence is governed by consistency and zero-stability, and its possible order is limited by the Dahlquist barriers.