Numerical Methods for ODEs Precision I have come across the following statement : Higher order (Ode stepper) does not always mean high accuracy (from Numerical Recipies, third edition). Why so ? Thank you in advance.

A high order stepper represents a fit of a high-order polynomial to the values in the stepper. Many times, these values have inherent noise from, e.g., roundoff error. A high-order polynomial tends to treat the noise as valid function behavior and will thus propagate those inaccuracies into the final solution. Low-order steppers, on the other hand, smooth out such noise.