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 - Higher Order Accuracy<br />
Second-Order Accuracy: T.E. ∼ O(∆x 2 ).<br />
Requires Two grid points, x i+1 & x i−1 .<br />
∂f<br />
∂x = f i+1 − f i−1<br />
2∆x<br />
+ O(∆x 2 ). (3.9 FP )<br />
Fourth-Order Accuracy: T.E. ∼ O(∆x 4 ).<br />
Requires Four grid points at x i+2 , x i+1 , x i−1 & x i−2 .<br />
∂f<br />
∂x = −f i+2 + 8f i+1 − 8f i−1 + f i−2<br />
12∆x<br />
+ O(∆x 4 ). (3.14 F&P )<br />
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