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 - Fourth Order Accuracy - Cont’d<br />
Rearranging the above equations and dividing by the<br />
finite-difference ∆x gives<br />
∂f<br />
∂x = −f i+2 + 8f i+1 − 8f i−1 + f i−2<br />
12∆x<br />
∂f<br />
∂x = −f i+2 + 8f i+1 − 8f i−1 + f i−2<br />
12∆x<br />
+ 4 5!<br />
∂ 5 f<br />
∂x 5 ∆x4 + H.<br />
+ O(∆x 4 ). (3.14 F&P )<br />
Fourth Order Accuracy: T.E. ∼ O(∆x 4 ).<br />
Requires four grid points to achieve the fourth order<br />
accuracy.<br />
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