Confusing velocity distribution result

In summary, the conversation involves a question about a diffusion equation and the use of second order in the obtained result. The speaker provides an explanation of "n-1" and attaches a paragraph for further details. The use of second order is due to the cancellation of first order differences in the equation. The questioner thanks the speaker for their explanation.
  • #1
zn5252
72
0
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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  • #2
What does "at n- 1" mean?
 
  • #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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  • #4
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
 
  • #5
I see. Thanks a lot !
 

1. What is a velocity distribution result?

A velocity distribution result is a graph or set of data that shows the distribution of velocities for a given group of particles or objects. It can give information about the average velocity, the range of velocities, and the spread of velocities in a system.

2. Why is a velocity distribution result confusing?

A velocity distribution result can be confusing because it often shows a complex pattern or shape, rather than a simple and predictable curve. This can make it difficult to interpret and understand the data, especially for those who are not familiar with the concept.

3. What factors can affect a velocity distribution result?

There are several factors that can affect a velocity distribution result, including the size and composition of the particles, the temperature and pressure of the system, and any external forces acting on the particles. These factors can cause the velocities to vary and result in a more complicated distribution.

4. How can I make sense of a confusing velocity distribution result?

To make sense of a confusing velocity distribution result, it is important to carefully analyze the data and look for any patterns or trends. It may also be helpful to compare the result to theoretical models or previous experiments. Additionally, seeking guidance from an expert or conducting further experiments can provide a better understanding of the result.

5. How can a confusing velocity distribution result impact my research?

A confusing velocity distribution result can impact research by making it more difficult to draw accurate conclusions or make predictions about a system. It may also lead to further investigation and potentially delay progress in a research project. Therefore, it is important to carefully analyze and understand the data to ensure the validity of research findings.

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