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Confusing velocity distribution result

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zn5252
#1
Dec2-12, 05:17 AM
P: 73
hello,
Please see attached excerpt of a solution to a problem. I do not understand why the result obtained is to second order ? (this is a diffusion equation they say)
Please let me know if you would need more info.
Thanks,
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HallsofIvy
#2
Dec2-12, 07:46 AM
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What does "at n- 1" mean?
zn5252
#3
Dec2-12, 09:13 AM
P: 73
n-1 means at the step which is prior to step n where n is the number of boosts . I have attached the first paragraph for more details.
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haruspex
#4
Dec2-12, 09:32 PM
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Confusing velocity distribution result

It's because the first order differences will cancel out: f(x+dx) + f(x-dx) ≈ f(x) + f'(x)dx + f''(x)dx2/2 + f(x) - f'(x)dx + f''(x)dx2/2 = 2f(x) + f''(x)dx2
zn5252
#5
Dec3-12, 01:18 PM
P: 73
I see. Thanks a lot !


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