Confusing velocity distribution result

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Discussion Overview

The discussion revolves around understanding a result related to a diffusion equation, specifically why a certain result is described as being to second order. Participants seek clarification on terminology and the mathematical reasoning behind the result.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the second order result in a diffusion equation and requests further information.
  • Another participant seeks clarification on the term "at n-1" used in the context of the problem.
  • A participant explains that "n-1" refers to the step prior to the current step n, which relates to the number of boosts in the problem.
  • One participant provides a mathematical explanation indicating that first order differences cancel out, leading to a second order term in the expansion.
  • A later reply acknowledges the explanation with appreciation.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical reasoning provided, but the initial confusion about the second order result indicates some uncertainty remains regarding the overall understanding of the problem.

Contextual Notes

The discussion does not resolve the initial confusion about the second order result, and the explanation provided relies on assumptions about the behavior of the function involved.

zn5252
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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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What does "at n- 1" mean?
 
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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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
 
I see. Thanks a lot !
 

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