Taylor Series Expansion
2016+Week4
2016+Week4
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Better approximations<br />
By using <strong>Taylor</strong> expansions for F( x 2h)<br />
and F( x 2h)<br />
, better approximations<br />
can be obtained:<br />
F'(<br />
x)<br />
<br />
<br />
F(<br />
x 2h)<br />
4F(<br />
x h)<br />
3F(<br />
x)<br />
2h<br />
O(<br />
h<br />
2<br />
)<br />
Forward Difference Formula<br />
F'(<br />
x)<br />
<br />
3F(<br />
x)<br />
4F(<br />
x h)<br />
<br />
2h<br />
F(<br />
x 2h)<br />
O(<br />
h<br />
2<br />
)<br />
Backward Difference Formula<br />
F'(<br />
x)<br />
<br />
<br />
F(<br />
x 2h)<br />
8F(<br />
x h)<br />
8F(<br />
x h)<br />
<br />
12h<br />
F(<br />
x 2h)<br />
O(<br />
h<br />
4<br />
)<br />
Central Difference Formula
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