It sort of sounds like you're confusing two different kinds of errors. Euler vs RK4 is an issue of truncation error. It's called that because when you approxima

It sort of sounds like you're confusing two different kinds of errors. Euler vs RK4 is an issue of truncation error. It's called that because when you approximate a derivative with a finite difference, you can see that you've truncated the infinite Taylor series. Truncation error is present even if there were zero approximation in the elementary floating point operations. I'm not sure how you mean that the difference between floats and doubles shows up with Euler methods especially. Under no floating point error, you can drive truncation error toward zero by driving the step size toward zero. But the floating point precision sets a floor on how low you can go. Perhaps this is what you meant.