Lotkins Bounds

We can find a bound for if we assume that the following bounds for f and its partial derivatives hold for

(3.37)

Where P and Q are positive constants and p is the order of the method. These bounds are due to Lotkin and are called Lotkin's bounds. Here in this example, we have

Hence from (3.36), we have

(3.38)

and we obtain the following bound for the principal local truncation error:

(3.39)