Local truncation error

Summary

The local truncation error of a method for an initial value problem is the error of one step started from exact values of the solution. It measures how well the formula of the method matches the differential equation, and it defines the order of consistency of the method. Together with a stability condition it controls the global error. For a one-step method with local error $O(h^{p+1})$ per step, the global error after $O(1/h)$ steps is $O(h^p)$. It is a special case of truncation error.