euler stepwise method

Dec 2008
288
13
not to sure how to do this question, thanks for any help
 

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Aug 2007
3,171
860
USA
Euler, without correction, is the simplest possible method of solution approximation. Are you SURE you are serious about this class? Really, if you are struggling with this, you will not be a happy camper at all in the real near future.

Just step through it.

dy/dx = 1 + xy

y(1) = 0

Then dy/dx around (1,0) is approximately 1 + (1)(0) = 1

y(1.1) = 0 + 0.1*1 = 0.1

The dy/dx around (1.1,0.1) = 1 + 1.1*0.1 = 1 + 0.11 = 1.11

y(1.2) = 0.1 + 0.1*1.11 = 0.211

The dy/dx around (1.2,0.211) = 1 + 1.2*0.211 = 1 + 0.12532 = 1.12532

Two things questionable with this presentation:

1) It was not necessary to calculate the last value. We were interested in y(1.2).

2) I carried all decimal places in all calculations. One may wish to concern oneself with proper significant figures. However, it pays to pay attention to all kinds of error.
 
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Dec 2008
288
13
haha cheers no its a first year class that i have to take and no im not to serious because after about two weeks i was pretty sure i wasnt taking the second year equivelent but thanks for the help!
 
Aug 2007
3,171
860
USA
Fair enough. Good luck with the one year, then.