Question: Numerical analysis - general question.

I am sorry, this question is not strictly related to Maple (but could be in some sense). If I am solving some simple system of ordinary differential equations I can obtain both analytical (symbolic) and numerical solution. Thanks to condition numbers I am able to quantify the error caused by rounding (in the analytical solution). Numerical methods make approximations and errors arising from them can be also computed (and in Maple can be controlled by abserr, relerr).

My question is: Can I quantify the total error (in the result) in cases when I am not able to obtain symbolic solution (and have only numerical solution)? By total error I mean "the error caused by rounding the numbers" + "the error of a certain numerical method"?

Thank you in advance for any suggestions.