Introduction to Numerical Methods/Introduction
Mathematical models are a central piece of science and engineering. Some models have closed-form solutions, therefore they can be solved analytically. Many models can not be solved analytically or the analytic solution is too costly to be practical. All models can be solved computationally and the result may not be the exact answer but it can be useful. George E. P. Box was right by saying All models are wrong, but some are useful. Since errors are inevitable a more practical question we ought to ask is how close the answer needs to be for it to be useful. In lots of engineering situations the only way to get the "right answer" is to use the following formula:
right answer = wrong answer + corrections
Missile Knows Where It Is is an audio click explaining how a missile guidance system can possibly work by repeatedly correcting it errors.
Before we discuss how to manage errors lets explore the sources of errors.