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 Difference: ∂f<br />
∂x<br />
Taylor Series <strong>of</strong> f i+1 & f i−1 at both x i+1 & x i−1 .<br />
( ) ∂f<br />
f i+1 = f i + ∆x + 1 ( ∂ 2 f<br />
∂x<br />
i<br />
2! ∆x2 ∂x<br />
)i<br />
2 ( ) ∂f<br />
f i−1 = f i − ∆x + 1 ( ∂ 2 f<br />
∂x<br />
i<br />
2! ∆x2 ∂x<br />
)i<br />
2<br />
+ 1 3! ∆x3 ( ∂ 3 f<br />
∂x 3 )i<br />
− 1 3! ∆x3 ( ∂ 3 f<br />
∂x 3 )i<br />
+ H,<br />
+ H.<br />
20