Slides - School of Engineering - University of Warwick
Slides - School of Engineering - University of Warwick
Slides - School of Engineering - University of Warwick
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3.3 - Central Differences - Cont’d<br />
Formula (3.6) is usually recast in the following form<br />
∂f<br />
∂x = f i+1 − f i−1<br />
2∆x<br />
+ O(∆x 2 ). (3.8 FP )<br />
This is a second-order formula.<br />
u<br />
u i+1<br />
Predicted du/dx<br />
u i<br />
True du/dx<br />
u i-1<br />
∆x ∆x<br />
∂f<br />
∂x ≈ f i+1 − f i−1<br />
. (3.8 F&P )<br />
2∆x<br />
Truncation Error:<br />
T.E. ∼ O(∆x 2 ).<br />
x i-1<br />
x i<br />
x i+1<br />
x<br />
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