Confusing velocity distribution result

zn5252

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,

HallsofIvy

What does "at n- 1" mean?

zn5252

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.

haruspex

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

I see. Thanks a lot !

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zn5252	Confusing velocity distribution result Tweet 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 Thumbnails

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	What does "at n- 1" mean?

haruspex Recognitions: Homework Help Science Advisor	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