Hey /sci/ I got a question for you. I've been reading up on rates of convergence and I can't seem to find anything that helps me with the specific problem I have.

Let's consider some ODE of the form: dy/dx = f(x) where f(x) can not be integrated analytically. We have a set of solution vectors evaluated computationally that approximate the solution for y, and the order of our approximation is n, so to obtain the solution vector for an nth order approximation we'd have yn. What I want to know is, since we do not have the exact function values, how would I go about testing the rate of convergence of a problem like this? I know for the specific problem I'm doing of this form there should be exponential convergence but all the graphs I'm producing are mega fucked up. The language I'm using to evaluate the approximations and the convergence plots is MATLAB.