[Thomashoffmann]

Hi all.
I need a little help to understand how to decide if a scheme is first or second order accurate.. My supervisor tells me that I can see it from the Taylor series formulation, where if I subtract eq 3.2 from 3.3 I get eq 3.4, which is first order accurate. and If I add them I get eq. 3.5, which is second order accurate.
This far I understand it, because the first and second order derivative skibs out when adding/subtracting...

But for my thesis I written that in a simple case of constant grid I can estimate T_e:
T_e=(T_P+T_E)/2
and I have written that it is a first order scheme. My supervisor tells me that it is a second order scheme. Why is that?
I just don't understand how to my simple case can be compared with a taylor series expansion?
Can one of you guys explain it better for me?
Thanks

Thomas