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 - Forward Difference: ∂f<br />
∂x<br />
Each node has one unknown variable associated with it.<br />
x 1 , x 2 , x 3 , . . . , x i−1 , x i , x i+1 , . . . , x N−2 , x N−1 , x N .<br />
f 1 , f 2 , f 3 , . . . , f i−1 , f i , f i+1 , . . . , f N−2 , f N−1 , f N .<br />
Finite Difference Formulae can be easily derived<br />
By replacing x by x i+1 .<br />
f i+1 = f i + ∆x<br />
( ) ∂f<br />
∂x<br />
i<br />
+ 1 2! ∆x2 ( ∂ 2 f<br />
∂x 2 )i<br />
+ 1 3! ∆x3 ( ∂ 3 f<br />
∂x 3 )i<br />
+ H.<br />
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