Taylor series for getting different formulas

[ericm1234]

I am trying to establish why, I'm assuming one uses taylor series,
\frac{\partial u}{\partial t}(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) )

 

[tiny-tim]

hi ericm1234!

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)) ? ​