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Taylor series for getting different formulas

  1. Feb 19, 2013 #1
    I am trying to establish why, I'm assuming one uses taylor series,
    [itex] \frac{\partial u}{\partial t}[/itex](t+k/2, x)= (u(t+k,x)-u(t,x))/k + O(k^2)

    I have tried every possible combination of adding/subtracting taylor series, but either I can not get it exactly or my O(k^2) term doesn't work out (it's O(k^1) or O(k^3) )
  2. jcsd
  3. Feb 19, 2013 #2


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    hi ericm1234! :smile:

    no you don't need taylor, just use the elementary definition of derivative (as a limit) …

    perhaps it's more obvious if you write (u(t+k,x)-u(t,x)) as (u(t+k,x)-u(t+k/2,x)) + (u(t+k/2,x)-u(t,x)) ? :wink:
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