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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3.4 - Higher Order Accuracy: O(∆x 4 )<br />
Second Order Accuracy: O(∆x 2 )<br />
∂ 2 f<br />
∂x 2 = f i+1 − 2f i + f i−1<br />
∆x 2 + O(∆x 2 ). (3.30 FP )<br />
Fourth Order Accuracy: O(∆x 4 )<br />
∂ 2 f<br />
∂x 2 = −f i+2 + 16f i+1 − 30f i + 16f i−1 − f i−2<br />
12∆x 2 + O(∆x 4 ).<br />
(3.32 F&P )<br />
Taylor Series <strong>of</strong> f i+N/2 , . . . , f i+1 , f i−1 , . . . & f i−N/2 at N<br />
points.<br />
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