Arthur Mattuck(MIT Math Prof.) said:....That's the usual way to do it. If you have the step size, since this is a constant, if I have the step size, I have the error, approximately. Have the step size, have the error. That tells you how the error varies with step size for Euler's method. Please understand, that's what people say, and please understand the grammatical construction. Since everyone in the math department has a cold these days except me for the moment, everyone goes around chanting this mantra.
This is totally irrelevant. This whole mantra, feed a cold, starve a fever. And if you asked them what it means, they say eat a lot if you have a cold. And if you have a fever, don't eat very much, which is not what it means at all. Grammatically, it's exactly the same construction as this. What this means is if you have the step size, you will have the error. That's what feed a cold, starve a fever means. And, remember this for the rest of your life. If you feed a cold, if you eat too much when you have a cold, you will get a fever and end up still having to starve yourself because, of course, nobody, when you have a fever, nobody feels like eating, so they don't eat anything.
All right, you got that? Good. I want all of you to go home and tell that to your mothers. You know, that's the way we always used to speak. Grimmer ones: spare the rod, spoil the child does not mean that you should not hit your kid. It means that if you fail to hit your kid, he or she will be spoiled, whatever that means. So, you don't want to do that. I guess the mantra today would be, I don't know. Okay, so the first line of defense is simply to keep having the step size in Euler....
I always thought that aphorism, "Feed a cold, starve a fever", was two separate phrases. That's interesting..