 For a sequence ("t""n") of values of "t", with "t""n" = "a" + "nh", the Euler method gives approximations to the corresponding values of "y"("t""n") as
The local truncation error of this approximation is defined by
and by Taylor's theorem, it can be shown that (provided "f" is sufficiently smooth) the local truncation error is proportional to the square of the step size