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For trapezoid and Simpson methods, the numerical integration have relative error where is the numerical result using intervals between [0, 1]. (i) Explain the power-law
For trapezoid and Simpson methods, the numerical integration have relative error
where is the numerical result using intervals between [0, 1].
(i) Explain the power-law scaling with an exponent 1.5 (instead of 2 and 4 as expected for the trapezoid and Simpson's method, respectively).
(ii) How can one circumvent this problem and restore the desired error scaling ?
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