Numerical Integration: Simpson's rule
Truncation error in Simpson's rule
Without proof we give the estimate of the truncation error in Simpson's rule for a 'neat' function on the interval \([a,b]\) with a partition into an even number of \(n\) sub-intervals.
Trunctation error in Simpson's rule Suppose that \(M\) is the maximum of \(|f''''|\) on \([a,b]\). Then we get for the result \(S\) of Simpson's rule with mesh size \(h=\frac{b-a}{n}\): \[\left|\int_a^bf(x)\,\dd x - S\right|\le \tfrac{1}{180}M(b-a)h^4\] In other words: the truncation error is a fourth power in the mesh size \(h\).
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