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Confusing velocity distribution result

  1. Dec 2, 2012 #1
    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,
     

    Attached Files:

  2. jcsd
  3. Dec 2, 2012 #2

    HallsofIvy

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    What does "at n- 1" mean?
     
  4. Dec 2, 2012 #3
    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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  5. Dec 2, 2012 #4

    haruspex

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    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
     
  6. Dec 3, 2012 #5
    I see. Thanks a lot !
     
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